One thing I managed to figure out is that the blinker side of socket doesn't work unless the headlight switch is on in either park light mode or all the way on in headlight mode. If headlight switch is off, then the blinker side doesn't do anything.
Sounds like either possible ground problem or someone wired the signals into the headlight circuit.
I don't think tail lights normally have anything to do with the signal circuit at all, and don't even run through the column/signal switch.
Try and find the wire that normally supplies the signal circuit and then see if it's connected to the headlights power somewhere.
Tail lights are easy since they only come on with the headlight switch.
