My right rear turn signal stays solid, won't blink, in the vehicle the right blinker light blinks excessively fast, I have a 1999 surburban

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.

If there is a bulb blown either in the right front or the right rear will cause this.Also check for good grounds on these bulbs.

Your right rear turn signal bulb is blown.Replace the bulb and the fast blinking will stop.

get the back working it will no longer fast blink change bulb and check with metre see are you getting power to it also check grounds

the fuse is broke

I would start by checking the blinker light bulb on the left side front and or rear,some vehicles will blink real fast and some wont blink at all when a bulb goes bad.

any increase in bink speed is direcly related to a bulb being burt out.

Replace the bulb that stays on and doesn't blink, if that doesn't solve the problem, let me know.

The blinker usually blinks fast when a turn signal light is burnt or not contacting. Check the signal bulbs to see if they are contacting or in good condition. If that is not it. Try replacing the blinker under the dash.

sounds like a bad ground through one of your lights, the right front or rear turn signal bulb.