Ahh grasshopper, how old are you? Once upon a time, many, many decades ago, autos were not operated and managed by semiconductors. For their ignition systems, they utilized mechanical components to control firing order, electrical energy created via a coil and condenser, points and distributor to send charge to spark plugs, etc. A rather short and simple explanation but you can do further research if really interested. Anyway, this old and antiquated system would not be subject to radiation damage. But, not to worry, I think very soon there will be oodles of info on the Internet on how to “rad-harden” your car. Probably will cause a run on aluminum foil....
I think the term is actually called “pre Solid State Ignition”.