I once made a similar project for our car, so the dome light would not accidentally drain the battery any more.
It used a 555 timer, relay, and large capacitor, 200 uF. The large capacitor allowed a 3 minute timing period.
It had only two wires. I installed it in the dashboard inline with the switch. It did not draw power until the switch was turned on. My project needed to be wired in the circuit directly, because I did want to wire it through the fusebox. I realized it had to get power even when the ignition was off.
I was just lucky that I could get access to remove the dome switch. It was a chore to install my circuit. I was just lucky there was enough space for it to fit.
The relay kept the light on for 3 minutes, then off. Very good. But then if the switch was turned off and on, the circuit kept the light on indefinitely.
So my project did not work perfectly. I think it had to do with the capacitor keeping its charge for a while after shutoff, and what point the trigger signal was applied to the 555.