Not a role playing game but a table top miniatures game. Well, I hesitate to say miniatures because I never played in a game that used miniatures. We used little card board cutouts, but that's just me being pedantic. There was GURPS Autoduel, but I don't remember whether you just ended up using the Car Wars rules when racing.
That's one of the biggest problems. The pilot obviously has a lot they can do with choosing where the vehicle goes, how fast it's going, maybe even being able to fire a weapon, etc., etc., but when you're a crewmember or a passenger there's typically not much for you to do. Rogue Trader from Fantasy Flight Games (based on Warhammer 40k) allowed multiple players to participate in ship-to-ship combat, but often there was only one thing for them to do every round. The priest in our group pretty much just rolled the same skill check every single round and was both tedious and repetitive.