How to deal with solitary party member?

Sooo, he doesn't mind sitting out the combat encounter with the seven other players having a good time? Then, I guess, there's no problem at all.
It also seems that in your games it isn't dangerous to go off on your own. If you want to discourage that behavior you may want to want to change that.

I've had a player in my campaign whose character was a one-trick pony with maxed out stealth skills. However, that also resulted in the character being mostly useless in any combat, even if he chose to participate from time to time (typically by shooting an arrow or two before going back into hiding). The other players soon learned not to rely on him. He did have some uses in non-combat situations, though.
The character eventually died during one of his excursions when he was located by a xorn (using its tremorsense) who grabbed him and burrowed, leaving the other party members clueless about his fate.

AbdulAlhazred said:

Don't let him take up more than 1/8th of the table time

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If he weren't doing what he was doing, the group gets more time. So 1/8th is too much, especially given whatever he's doing, doesn't seem to be interesting to either the DM or the other players.

I think this is a difficult problem that all DM's have to deal with eventually. In my opinion, there are three ways to approach this:

If the player is deliberately constantly splitting up, then discussing it outside the game would be a way to go. Explain to him that it is a team game, and that if they try to stick together, the game is a lot easier for you to run. It also isn't very enjoyable for players to wait for the combat of another group of players. It should not be fun for him when he has to sit it out, nor is it fun for the other players when it's just him versus a monster. The game isn't always about "what your character would do", but also about "what is the most enjoyable for everyone at the table". It's a cooperative game in more ways than one.

Another way to approach it, would be to allow it, but to conveniently have characters (players and npc's) meet him at the same location. This is a technique I use all the time, and the players know I'm doing it. I take some narrative license as a DM to conveniently have the paths of different characters cross at the same time, so they are together again. So if your player happens to decide to go on a trip to the local church... guess who happens to run into him at that church? Of course, it's that good old npc that they met earlier... he just happens to be there. And this npc may just relay a piece of important information that is really crucial for the other players to know, thus giving him a good reason to rejoin them!

A third way would be to allow the PC to sit an encounter out, but to have the player take control of an npc during the fight that his allies are involved in. So while his character isn't present, he still gets to participate in the fight. I ran into a similar situation in one of my campaigns:

"All of the players decided to drink from a magical lake, to partake in a magical ritual that put them in a deep slumber... that is, all players except one. But I still had this player take part in the dream-trial that followed, but as a spirit guide. He got to take all the same choices as them, and show what happens when that choice is made. But at the end of the trial, everyone woke up next to the lake, and he was the only one who had no recollection of the event (because he never really took part in the ritual)."

I think that this has to be an out-of-game discussion. I generally outright tell my groups that they need to stick together. If a PC wants to go do a specific thing, they need to get buy-in from the rest of the group to do it. It’s no fun for the rest of the group to just sit there while one person does the thing for 5+ minutes.

In most cases, I’ve found that players that do this are just looking to get the narrative focused solely on them. That’s not always a bad thing, but to force it to happen is disruptive.

Outside of outright telling the player in question not to do it, I find the best option is to get the excursions over as quickly as possible. And if they keep doing it, I make them as boring as possible. Maybe just a sentence of description. If someone's deliberately making my job more difficult, I don't think I owe them much more than that.

I left it open for the party to split. And some people went with him at first, but then when the sound of fighting started they ran back to help the team, where he didn't. He just kept progressing the opposite direction.

And in a different campaign, he specifically left without telling anyone, or letting anyone know. Like he specifically did it by himself, for the purpose of doing it by himself.

Now that I think about it, he specifically went off by himself in 2 other campaigns also.

Ironnipple said:

So he technically should trigger some encounters, but then he would be entering an encounter designed for 8 people by himself.... Should I just let him do that and most likely die...?

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Yes.

When a player starts going off on his own or turning 'chaotic-everywhere,' chances are he's not getting the amount of personal attention from you he wants - that seems doubly in that you already have 'too many' players (4-6 is an ideal RPG group size, IMX), the larger the party, the longer it takes to get back to a given player's next turn, and the more likely they've lost the thread of what's going on by then, forcing you to re-cap and explain and making each turn take even longer.

The best solution really is a smaller group.

Tell him to make characters that stay with the group or he can leave the game.

He's a problem player and you're group is plenty full of people who seemingly are not.

Tony Vargas said:

Yes.

When a player starts going off on his own or turning 'chaotic-everywhere,' chances are he's not getting the amount of personal attention from you he wants - that seems doubly in that you already have 'too many' players (4-6 is an ideal RPG group size, IMX), the larger the party, the longer it takes to get back to a given player's next turn, and the more likely they've lost the thread of what's going on by then, forcing you to re-cap and explain and making each turn take even longer.

The best solution really is a smaller group.

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Yeah, there's definitely something he's not getting with the group. However, the fact that he's got a history of doing this tells me that he's got some sort of personality characteristic, or agenda, that is driving him into this counterproductive behavior.

Frankly one solution is just to ignore it. If he wanders off then just continue to run the adventure for the rest of the group. Maybe when there's a break or something you can discuss with him what happened to his character. Perhaps he'll meet up again with the rest, or some fate will befall him, etc. but you don't really HAVE to spend time on it. You can always explain that its onerous on everyone else to handle his solo side adventures during regular table time and you'd prefer to do it some other way, before, after, in email, on a lunch break sometime, whatever.

If his choice is basically to spectate or rejoin the group, then I think eventually he might just choose to rejoin.

"But it's what my character would do!" is a red flag of future non-cooperative behavior.

You have to talk to him away-from-table (and not right after he does it). If you have another player who is a good diplomat (IRL), it may help to bring him/her into the conversation.

If he's stubborn, let him know that he can trigger encounters, traps, &c while alone - and the group may not be able to help. 8-to-1-against odds are not good for the character's survival.

If circumstances require that he make a new character, tell him - be as unemotional as you can - that his next character must be the kind that "working with the party" IS "what he would do".

Don't be afraid of dropping ultima ratio regnum* (if nothing else works): if he continues to disrupt the group's efforts, you will stop inviting him to sessions.

* 'the King's final argument', slogan cast into the side of a cannon in the 1500s.

Overlooked this somehow:

Ironnipple said:

So he technically should trigger some encounters, but then he would be entering an encounter designed for 8 people by himself.... Should I just let him do that and most likely die, and hope he gets the idea to stick with the team? Or what....

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That is exactly what you should do.

Why adjust your challenges if the PCs are being stupid? Let the players learn from their mistakes. My motto is that a dysfunctional party is a problem that solves itself. Normally it shouldn't take more than one TPK to get their attention... And if it's just a single PC that is being stupid, it's even less of a problem. I recall one of my players' PC(s) dying three times in a single adventure: First he tried to charge over a hanging bridge while goblins at the other end were ready to destroy the supports, then he trampled into a grey ooze, and finally he tried to argue with a roper that had him firmly in its grasp (in case you're wondering: we played the D&D 3e 'Forge of Fury' module).
He became a lot more careful after that, although he still managed to accumulate the most character deaths at the end of the campaign.