the lights are connected to the light switch

you must have some wires in the wrong place so the turn switch is feeding thru the light circuit
"dual sockets" in the front lamps or
dual filament bulbs? separate wires to the front lights all the way from the signal unit? if the tail lights aren't working properly [with light sw in parking light position] you must not have done the tail wiring right so the park light circuit is tied in to the signals somehow .... did you use
the tech tip to check over the wiring?
Bill