Turn signals front and rear function like normal when headlights are off and when parking lights are on, but as soon as headlights are turned on, the left front turn signal fails to operate at all. All other lights work fine with headlights on.
That sounds like a ground problem at the left front lights. The ground terminal on the headlight socket should have 2 black wires. One goes to the ground on the parking/turn signal light socket. The other goes to a ring terminal that's grounded to the radiator support with a screw. Remove that screw, and clean up any rust/corrosion that's present on the terminal and around the hole before re-attaching it. There might be a star toothed lock washer in between the ring terminal & radiator support ... if so, clean that up and put it back into place.
With a bad ground at that location, the parking & turn signal lights can still find an alternative ground path through the headlight filaments. But that alternative ground path goes away when power is applied to the headlights.