Ah, they used to make such switches. Leaf switches (I think NJ International made them) one set of contacts was momentary (in passing) and the other sets would hold the signals and indicators.
Oh, that brings back memories! I used to have a bunch of them back in the 1970s. Used one to make a throttle. Loved the smooth spring loaded action of throttle in one direction, brake in the other direction. Also used a bunch of them to make an audio control panel back then. Must have thrown them out over the years because I don’t have them any more.