If I connect the outbound parking light wire to the outbound headlight terminal those lights work.
I assume you mean you moved the wire on the switch from the front parking light terminal to the head light terminal. You are aware that the front parking lights are supposed to be off when the switch is pulled out all the way as 4onthefloor mentioned earlier?
Do the tailights work? I connected my front parking lights to the same terminal on the switch as the taillights and leaving nothing connected to the front parking light terminal. Doing this means that the front parking lights will not switch off when the head lights are on.
It sounds like your ground is OK and the wiring from the switch to the bulb is OK.
