Turn indicator lights acting up

Hi all,
I have an annoying problem with my 63 Dart's turn indicator pilot lights. The pilot lights flash simultaneously and kind of dim. The signal lights work normally, both front and rear, left and right. This occurs only when the headlights or parking lights are on, lights off everything's normal.
I tried to read the wiring schematic but could not figure out anything. I think the fault cannot be in the turn switch as they work fine when lights are off. Any ideas what to check?