Here’s a bit of the US Code Title 10, A, II, 49, Sec 973 yadda yadda yadda dealing with officers holding elected offices.
Basically, there’s a few restrictions–the most obvious of which being, that it cannot interfere with the military duties required. I would imagine anything outside of a municipal function may get to be too much of a hassle to juggle both jobs at once, but hey, some clowns can juggle pretty well.
But, take it FWIW.
Tripler
I can juggle too. But I prefer the term “court jester”.