Your car has a bad ground connection. Check the ground wire (probably green or black) leading from the rear left taillight assembly to the body of the car. I think you'll find that the connection is either loose or corroded where it attaches to the body.
Usually the fuse is going bad.
1989 silverado left turn signal set applying brakes causes the left turn signal to dim and the two right rear tail light bulbs to alternate brightly? Further problem occurs to same truck - in Park and brakes not applied -- if head lights are on turn signal flash slows right down almost to a stop and becomes very dim
if your signal is faster than normal then you need a new bulb
You may have a "ground loop" problem on the left turn signal. Check the ground wire at the front and rear signal bulbs.
It looks like your left front one is burnt out. When there is not enough current flow the good light will not flash.
Normal cause is failed bulb.
light is burned out
flasher will not flash when circuit is open or shorted replace left front turn signal bulb
need to replace blinker bulb
You have a failed bulb on the right side.
was jeep in accident and repaired? sounds like crossed or shorted wires
Could be a burnt out bulb or a bad flasher unit.