In the Park location, you should get TAIL and Gauge lights only. Its a side-of-the-road emergency stop lighting scheme.
Your key should have 4 wires, RED, BLACK, BROWN, and BROWN/WHITE. BROWN should be for TAIL. BRW/WHT should be for front end gauges, RH switch. BLACK is for switched 12v, coils, KILL/RUN, HORN, etc. RED brings power from the battery.