When John Wilkes Booth, fleeing from his assassination of Lincoln, was surrounded in a burning barn, one brave Union soldier disobeyed his orders and shot to avenge the President, right there and then. That man was Boston Corbett.
"Gee!" you might be saying to yourself. "What an impressive record! I wonder why I've never heard of this interesting fellow?"
Well, you see, Corbett was mad as a hatter. Literally--he started life as an apprentice milliner and (after a short stint of alcoholism ended by becoming a born-again Christian) worked his way up, and the brain damage from mercury fumes is probably responsible for some of his erratic behaviour, such as castrating himself after being aroused by prostitutes. At home. With scissors.
After joining the Army, he was nearly court-martialed for telling his colonel off for taking the Lord's name in vain, then re-enlisted, then captured and sent to notorious death-camp Andersonville, and then later released. This was probably quite bad for his mental health as well.
He did then get a second court-martial for the whole "killed Booth before he could stand trial" thing, but the Army decided to release him on the basis of "oh dead how sad never mind". The brief intense fame that surrounded him turned out to be something of a nine days wonder, and he retired from the Army and public life soon afterwards.
He went on to never hold down a steady job due to his own religiosity and erratic behaviour (convinced a secret society trying to avenge Booth was after him, he started brandishing a pistol at all times) before being appointed assistant doorkeeper to the Kansas House of Representatives, a position he resigned from after paranoidly chasing several officers out of the building, being declared insane, and then escaping from the insane asylum he was committed to and eventually dying in a forest-fire in Minnesota. We think. It's unclear.
Is there any chance this man could have gone into politics? Honestly, bar an incredibly Big Brained Move by the Republicans in a TL where Booth's plot killed Seward and Johnson as well, it seems unlikely. On the other hand, such a fantastically distressing historical figure deserves to be more well known.