The leakage current of a tantalum cap could cause timing variations with an 8.2M resistor. It would be better to operate the 7555 as a higher frequency pulse generator, which allows the use of a smaller resistor, and run the pulses into a counter, such as a 4060, to get the longer times.
The switch data is indeed confusing. It looks like there should be two terminals for the LED and two for the switch contacts.
The automobile electrical system can have large voltage spikes and transients due to such things as starter operation, so you should decouple the power to your circuit with a small series resistor and a large capacitor to ground, with perhaps a 15V zener to ground also. Otherwise you should be able to use a 12V relay. Relays are very tolerant of voltage variations.