Right rear tail light is staying lit with all switches disconnected...original problem was tail lights on all the time.Switched out turn signal switch,ignition switch and brake switch

Usually if my right blinker is flashing fast it means one of my right blinkers is not working either front or back right side. Not sure but I know every vehicle I have ever had was like that. One blinders not working the other flashes fast, on the dash also.
This post he repaired the problem it was the light switch.
Right rear tail light stays lit, won't turn off
https://www.bimmerforums.com/forum/showthread.php?2301226-Rear-tail-light-stays-lit-won-t-turn-off

Generally speaking, symptoms of a bad or failing turn signal bulb are usually the culprit...in your case, either it's the front left or rear bulb. Varies for different vehicle makes...common signs include:

1. turn signal light staying on solid
2. or blinking very fast
3. or either sides of the bulbs stop blinking altogether.

To test this, make sure you reconnect everything you disconnected.
Turn the left signal light on; go to the front of the vehicle, is the turn signal bulb illuminated? If it lights up, even though it is not blinking obviously the bulb is okay. If it doesn't, replace it- problem solved. You'll do the same procedure for the rear turn signal Is that lit up? If not replace the bulb and the problem is solved.
Another common failure is when the turn signal blinks really fast, same procedure as mentioned above.
If both bulbs for the left side and right side illuminate but don't blink, the problem is in the steering column turn signal switch.
If the left or right side blinkers don't work properly at all...then check the integrated hazard warning/turn signal flasher relay- that may be defective; again, that's usually the case if both sides of the signal light don't work.
If you are blowing any fuses related to the flasher system, you have an electrical overload in the turn signal circuitry.

fuses blow because of dead shorts or excess current draw
to blow a 15 amp fuse indicates a dead short
by disconnecting the rear lights , the problem is in something else you have replaced
could be a problem in the head light wiring

check for poor ground i wiring it mite be using the signal wire for a ground

If the indicators on the dash are staying lit all the time, it is because you likely have a bad ground to one of your running lights, causing the running lights to ground through the turn signal circuits. This is often caused by either a bad socket assembly at one of the bulbs or an incorrect bulb is installed in one of the sockets. You need to check FRONT and REAR lights to see which one is not working correctly. Also check the running lights and marker lights on BOTH sides of the vehicle. There will be SOMETHING that will not look the same from one side to the other if the left side is working correctly and the right side is not. Please keep in mind that you cannot use the right REAR turn signal without also using the right FRONT turn signal. The problem could be at EITHER end.

either a stop or turn signal or tail lights are out

The brake light and the turn signal are the same bulb. Most of the time if the bulb on the dash stays on it is because a bulb is blown and thats the way it tells you.

Rear lights are double filament bulbs one side for the lights other side for the brake/turn signals so it still may be a bulb. Do u have a test light or volt meter you can check to make sure u have power there when brakes or turn signals are activated. Or just try another bulb.

no disrespect but....
Check the book and make sure you are using the proper bulbs on all sides. (3957 looks just like 3956 but wont work right)