How does someone get an assignment as an aviation accident investigator?

Last I checked, its officers usually and they get basically called up to investigate. Any info you need will be through Rucker for sure

Call the Safety Center at Rucker. The Safety Center, like the NTSB, has a GO Team for High profile accidents. I was fortunate enough to go through the Aviation Safety Officer Course in '88. By that time, I had already served on several Aircraft accident investigation boards. AH-1 at 2/9 Cav, UH-60 from the 160th, an OH-58 x 2 mid-air collision at the NTC, and a UH-1 Medevac CFIT accident at the NTC. All of this aided me as well as being an Instructor Pilot for my second career as an Aviation Safety Inspector (Air Carrier and General Aviation) with the FAA. There I investigated several dozen fatal and non-fatal aircraft accidents. These were separate but usually investigated in conjunction with the NTSB.

I don't think there's an actual assignment for it. Typically they select people from the units in the nearby areas. Because I've seen officers selected to investigate incidents at another unit who had no idea what it was they should be looking for and I explained what to look for and the questions to ask.

I'm not sure if it has something to do with the billet they currently hold, but if anything, I would consider talking to your unit's safety officer. They might have a better answer.