This is one of the reasons I'm not so fond of DEADLY STATE OF MIND, as opposed to the actual quality of the episode. Even though Dr. Collier is an opportunist of some kind who's afraid of that getting out, I can never help thinking, "If only he'd confessed to the original killing, things might have worked out for him." The same thing is true of DAGGERS OF THE MIND, but it's maybe even more true of that one, considering what he was interrupting when he committed the killing. (Especially if there had been women or pro-feminist men on the jury!)
Plus, even though he's in only one scene, I think it has nearly the most dislikeable victim of any episode (the original victim, I mean). In BLUEPRINT FOR MURDER there's a similar situation, but at least Bo tears into Elliott without being nasty to his wife for LIKING Elliott (let alone in a physical way).

Bravo. Good questions. Why DID they not confess to the initial crimes, which were technically not murders? I suspect that as first offenders who could prove the homicide was an accident they would not get a stiff penalty.

It makes me wonder if I would confess.

Brimmer was indeed guilty of involuntary manslaughter. If he kept his cool he could have had the victim charged with criminal trespass.
Brimmer would have also been charged with abuse of corpse for dropping off the dead body and probably hindering apprehension.
Outside chance he could have received probation based on his lack of criminal record, but he more than likely would have received jail time.
More than likely the latter mentioned charges in conjunction with the involuntary manslaughter offense would have sunk his chance of a probation sentence.