Blinkers AND taillights has got to be either; the bulbs, their installation,or the body ground.
A dual filament bulb has a very particular installation orientation.
Single filaments not so much.But the leaded contactors have to be in good condition and clean.
If the front blinkers come on, and the dash indicator lights up, then the front body ground is working , so the problem,exclusive of the above, could be the ground right at the rear sockets.IMP this is the most likely.
Oh yeah, I have seen this problem in the fuse box, where water got into it on the back side and corroded the fuse clips. So even tho the fuses were good, they were not connecting. Heck of a job to clean up.