I assumed that on a presidents death an election is held and that the president that won the closest OTL election will win it.
Someone else is doing the day to day business for old/incapaciated presidents but formaly they remain in office (no resignations).
Nixon can't comit Watergate ITTL and is therefore not impeached.
Note the Adams dynasty.
20 years of Truman are (from my outside perspective) totally worth the other shit.