If the relay clicks, but the solenoid doesn't activate, it could be - in no particular order:
1. Bad solenoid.
2. Bad ground. (The solenoid gets its ground through the trunk latch "loop", when the lid is closed.)
3. Bad connection / wire. I have seen the 12V wire broken where it goes through the rubber grommet at the front corner of the decklid.
4. Bad relay. (The "switched" side contacts could be burned. It does happen.)
If the relay does not click, it could be bad, or the switch could be bad.
I'm not sure about parking brake or gear selector requirements, since my car has been swapped from auto to manual. Mine works all the time.