What do aircraft accident investigators do in between incidents? Consider aircraft accident investigators in your average first- or second-world nation. Something like the US NTSB, the French BEA, the Canadian TSB, the Australian TSB, ... (whichever you happen to be most familiar with is fine)

Now, most of the time, aviation ticks along nicely. Aircraft take off, aircraft cruise, aircraft land. Aircraft are checked up and maintained. It's not like you are going to call in an accident investigation team for a hard landing or a broken light bulb.

Yet when something does happen (especially in a known location) that warrants an investigation, investigators are on the scene quickly, not uncommonly within hours of an incident.

Considering how long investigations can take to complete, it seems likely that multiple teams would be needed, so that one can be brought in quickly without unnecessarily disrupting any ongoing investigation. (Aircraft incidents do, unfortunately, happen more often than once every several years, especially in large countries with significant amounts of air traffic.) On the other hand, incidents happen rarely enough that it seems to me, most of the time, a large number of such investigators would basically be sitting around just waiting for something to go wrong. That doesn't seem reasonable, so...

What do these people actually do while aviation pretty much just works?
NTSB investigators handle General Aviation incidents that you never hear about, as well as the Commercial incidents that make the nightly news.

There are new incidents every single day.
Try reading AVHerald for a sense of what happens, or searching the NTSB Aviation Database.

They have plenty of work.