In the two parter 'Fade out, fade in' in MASH we see that Klinger enlists the services of a 'lawyer' to get him a section 8. Although this fails, out of universe, was this an attempt, at least initially, to 'kill off' the character of Klinger? Are there indications that Farr wanted to leave the show at this point?
It's possible. This interview doesn't specifically state the timeframe that he's discussing, and I don't recall when that episode aired, but Farr does discuss that he asked for a raise and the studio's typical response was to write a character out of a show rather than give in to the actor's demands.
But, at the same time, Walt is correct in that for the majority of the show, Klinger was trying his best to get a Section 8 dismissal. At some point, after a discussion with Col. Potter, he stopped trying to do that.
The interview is here (and should start up at 29:08, where Farr talks about asking for the raise).