Sorry, but can you explain how characters do something without the players saying they do it?
To be frank, this and [MENTION=71699]clearstream[/MENTION]'s examples are "I want to be able to use the mechanics to be 100% sure, with no risk, that I can treat another as if they are bad."
Would you be okay with an insight check that, if failed, means you must 100% and with utter, unshakable conviction believe the other character is telling the truth? No, what insight represents is a risk free check to establish the proof to treat another as a bad actor, in this case a liar. That's not interesting enough for a roll.
One distinct use of Insight, called out in the RAW, is to determine true intentions, such as when "searching out a lie". A good mechanic to apply in my case is a Contest: Rogue's Wisdom (Insight) against Barbarian's Charisma (Deception). A DM might arbitrate as follows -
If B's result is higher, then R is deceived into believing that B thinks she's presenting the truth. "
You trust her on this score; she's on the up-and-up."
If R's result is higher, then R's perspicacity reveals whether B thinks she's presenting a truth, or a falsehood.
On a draw, things stay as they were (no information, either way).
The Contest result is uncertain, unless there is a disparity of 20 points between the characters (so that a draw is ruled out and one or other always wins). The result is interesting because players have said that their characters care about it. Perhaps they want to know if the Barbarian is planning to sell them out to the evil Sorceress?! The risk, for B, is being seen through. The risk, for R, is having to believe that particular lie. Regarding "
unshakable conviction". I don't think a single contest should usually lead to "
unshakable" convictions, but this could be a good place to use optional rules such as Degrees of Failure from the DMG.
A DM might choose to make these rolls on behalf of the players. The benefit is obvious if the liar gets the higher result: it prevents other characters treating "deceived" as equal to "no information". Unfortunately it penalises the character using insight, because they can't differentiate a getting the lower result, from getting the higher result where the other character also turned out to be honest. My experience at the table has been that it's usually more fun just to let players make their own rolls, in the open.