my camaro had the same problem light was good but woulnt work it was to much grease in the socket who knew The turn signal flasher is most likely defective. The one on the fuse panel is for the hazard flashers. the turn signal flasher is to the right of the steering column on the backside of the dash.
The turn signal relay for a 1981 Camaro should be mounted in on the fuse box. It is on the upper left hand corner.
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
need to replace blinker bulb
flasher will not flash when circuit is open or shorted replace left front turn signal bulb
Most likely your wires are crossed.
You have a failed bulb on the right side.
was jeep in accident and repaired? sounds like crossed or shorted wires
may have bad bulb
Could be a burnt out bulb or a bad flasher unit.