Hot water to unjam trigger shifter

It could hypothetically help get them working, but at that point you'll have washed out a bunch of whatever lubricant remains and should replace it with something anyway.

When they stop working, the most common problem is that the grease around the pawls has gummed up, keeping the pawls from being able to spring up into their extended position where they can catch on the toothed ring. The first thing to do is remove the cover (don't disassemble them any further than this), find the pawls, drip some oil (whatever you use on your chain is fine) around them, and work them back and forth with some kind of pointy tool. The vast majority of the time, unless there's a broken spring somewhere that renders them non-fixable anyway, this approach will fix them.