well, the only suggestion that spring to my mind is to use 2 voltage source. 12V constant from battery for the PIC, switched 12V for the rest of your unit. You can also use the switch 12V to turn your PIC into SLEEP mode.... in this case it will get few uA from the car battery + few mA for voltage regulator... 78L05 in TO92 need less minimum current than 7805 in TO220 package.

Usually car cluster work almost like this. There's alway one constant 12Volt going into.

That way, you will be able to do what you want. Will be easier to save data to EEPROM then switch off external stuff(LCD,BacKlite...etc), then turn to SLEEP mode.