Left blinker flash fast, hit brake left blinker goes out left taillight goes out but both backup lights come on

You obviously have a bad connection somewhere in the taillight. Some trucks it is a common problem and the taillight circuit board is the problem.

find and fix the faulty ground wire

You must have one of the blinkers out have you checked the wing indicator or the earths or relay switch??

ck fuse for rear taillights tis under the dash lower left of steering wheel. or if you still have the manual look in there under fuses.
also look for a bad ground but i doubt that.. if it's both rear out.
fast flashing well here's a chart with all sorts of info.
Problem What To Do Turn signals light, but do not flash Replace the flasher No turn signals light on either side Check the fuse. Replace if defective.
Check the flasher by substitution.
Check for open circuit, short circuit or poor ground. Both turn signals on one side don't work Check for bad bulbs.
Check for bad ground In both housings. One turn signal light on one side doesn't work Check and/or replace bulb.
Check for corrosion in socket. Clean contacts.
Check for poor ground at socket. Turn signal flashes too fast or too slow Check any bulb on the side flashing too fast. A heavy-duty bulb is probably installed In place of a regular bulb
Check the bulb flashing too slow. A standard bulb was probably installed in place of a heavy-duty bulb
Check for loose connections or corrosion at the bulb socket Indicator lights don't work in either direction Check If the turn signals are working
Check the dash indicator lights
Check the flasher by substitution One Indicator light doesn't light On systems with 1 dash indicator:
- See if the lights work on the same side. Often the filaments have been reversed In systems combining stoplights with taillights and turn signals
- Check the flasher by substitution On systems with 2 Indicators:
- Check the bulbs on the same side
- Check the indicator light bulb
- Check the flasher by substitution
hope this helps. may want to print for future reference. :)
hope this helps.

because of no light flasher on left side the front one will go faster .maybe the left rear light is burn. and brake lights are control by the brake switch on brake pedal hardware, might be unadjust

The Bulbs Have 2 filliments in them if 1 is burnt out that would give you the fast not working tail light there may be an issue with the brake light switch located above the brake pedal on the arm.

sounds like the relay has shorted,need to fit new.

you got a bad ground on the taillight circuit

You will need to replace the rear light assembly that was melted.

you have a back break light out