Left blinker does not work when the running lights are on

Bad ground on the non-working lamp.

May be as simple as remove and reseating the blub.

WHY.
When running lights OFF the turn signal works because it grounds through the running lights via the common (Shell) connection on the bulb.

With the running lights ON the DIMMER element in the lamp does the same via the turn signal lamps but when both are "Lit" There is no ground.

Start by removal and re-seating of the bulb. Then start chasing fora bad ground on that socket.