Something changed if it was all working then quit. You need to figure that out.
The rear tail light housings are grounded through the mounting bolts to the rear 'bumper'.
So the GW wire from the flasher is going to the B terminal on the turn signal switch?
Where does the 12V wire go? Fuse panel?
Is there a separate ground wire for the flasher or is the case just grounded?
Can you take pics of all this?
When the right turn is on and working properly, does the flasher get hot?
Something on the left side is pulling a lot of current to get the flasher hot. A fuse should have blown somewhere. What size fuse does the +12 go to?
Oh, BTW that is NOT an OEM flasher.