i'm not sure that head unit has a true remote turn on. the OP needs to get out his volt meter and test Pin #5 to verify if it is on with other sources - assuming it's not just AM/FM. that radio looks very basic, and old.
what make/model is it?
if you'd have a true remote turn-on and pin #5 loses voltage when switching to other sources - you either need a LOC with auto-turn on (you obviously need a LOC anyway) or you can get a switched ignition +12V from the radio ignition wire - with a 1A fuse and a toggle switch on the dash. the toggle switch is to turn the amp off when the radio is off while the car is on.
remember -
amp on last, amp off first.