Do the running lights and reverse lights work normally?
If so the first thing I would suspect is that the bright filament is burned out but the running light filament is still good. The running lights and brake/signal lights use the same bulb, but with 2 filaments, like the old 3-way incandescent bulbs people used to put in household lamps. The solution would be to replace that bulb.
If none of the lights work correctly, it is likely a grounding issue caused by lack of metal on metal contact through the bolts. Fixing the bolts would likely fix the problem.
As for the bolts, my guess is that the nutserts are missing or stripped out. Remove the assembly and take a look at the holes where the bolts go in. There should be a piece of metal called a rivet nut or nutsert with threads in it. If the rivet nut is missing, loose, or stripped, it will need to be replaced or substituted. If you’re not sure, take a picture of the three holes and post it here
No I do notDo you have a light guard over the tail light preventing a solid ground?
The light is the whole assemblyAre the LEDs bulbs or is it a new tail lamp assembly?
Did you get a LED compatible flasher relay? (Installs under the steering wheel)
If the running/reverse lights work, it’s not likely a grounding issue. You could run a wire from the bolt holes in the tail lamp assembly to a ground point on the body, but that likely won’t help you here.
Check inside the assembly to see if there is a continuous piece of metal that connects all 3 bolt mounting points together. If this is the case, any one bolt should be able to ground the assembly.
Do you have LED front turn signals or sidemarkers?
If you still can’t figure it out, it may be worth checking the wiring harness connecting the tail lamp assembly with a voltmeter with the brake pedal depressed to ensure the brake light voltage is normal. That would eliminate the likelihood that the issue is further up.
You might even be able to check if the taillight assembly is bad by plugging it into the harness for the other side. I seem to recall the left and right harnesses being the same. Note that it has to be at least partially bolted in or grounded via some other means to light.