To take these one at a time...
Is Eeyore an incredibly shy player who you are trying to slowly coax out of his shell to become an awesome roleplayer sometime in the future?
An incredibly shy player most likely would not have done what Eeyore did here; he'd instead have not wanted to make waves and gone along with the plan - and by his shyness possibly saved some characters' lives!
Is Eeyore a brand new player who is paralyzed with indecision about how they should be playing the game and it is a learning process for them -- they promise they will try to do better next time?
Eeyore might be a brand new player (for my example I was assuming all the players had been around a while but I don't think I mentioned it) but certainly in my example isn't paralyzed by indecision; he instead made a series of clear decisions - to go for the princess instead of help with the dragon, to lie about failing his attempt at the lock, etc. - on the fly. That said, if Eeyore *was* being run by a brand new player I'd probably cut more slack for him, in full knowledge the other players would probably sort him out over time.
Did Eeyore just get fired from his job and turned inward this game, but you know he's made a good showing during most other games?
I put my example probably in too much isolation. Fred, the same player's last character, was - let's say for these purposes - a fine contributor to the party; but Fred's death put the player into survival mode as evidenced by what Eeyore did here.
Is Eeyore someone who need to have 'The Talk' with later in the week, but you absolutely don't want to start any drama tonight?
Depends on my role. If I'm the DM it's flat-out not my place to tell Eeyore's player how to play his character; my role is to remain neutral and referee what's put in front of me. If I'm Bjarnni's player I've already said my piece in character, I probably don't trust Eeyore much any more and will proceed on that basis, but I'm otherwise set. If I'm one of the players who just lost a character I'm either going to bitch now or hold my tongue and see what Eeyore does next - is this a pattern or a one-off. I-as-player also have to keep in mind that whatever I roll up next is probably going to have to be acceptable to Bjarnni and Eeyore, as they're doing the recruiting, unless the DM drops the new characters in their laps somehow. But if Eeyore hangs me out to dry...
That said, if I'm the DM and Eeyore intentionally maintains this pattern I realistically have to be ready for some in-character retribution against him later; for example if in the next adventure he hangs Bjarnni out to dry and Bjarnni survives I can't as DM tell Bjarnni's player he's not allowed to have Bjarnni run Eeyore through. In fact, if I-as-DM have rules against PvP
I'm actually enabling Eeyore to do what he does as I've arbitrarily neutered his greatest deterrent.
Lan-"I also forgot in my earlier example to note that Bjarnni and Eeyore gained even more wealth via looting their ex-comrades"-efan