Why when my i turn my left turn signal on, both rear brake lights blink

The high mount brake light gets its own signal from the brake light switch (on the brake pedal). Or at least the wire leaving the brake light switch will splice, one wire to the high mount brake light, and the other for the rear brake lights is routed through the turn signal switch, and coordinated there with the turn signal wires to the rear brake lights. The brake wires and turn signal wires share the same wire, and same filament in the bulbs. It is kind of complicated, but brakes applied with no turn signal, brake light wire goes from brake light switch through the turn switch and out to the bulbs. If brakes applied with turning signal, non blinking brake light wire goes from turn switch to rear light, while the turning signal wire will go through the flasher relay, and then to the rear light to cause blinking.

I hope that makes sense. It appears the problem may be in the turn signal switch for both the turn signals and the rear brake lights.

Has the vehicle been in an accident on the left rear side. First check the bulb to be sure it is not defective, trade it out with the side that works properly to test. If the bulb works well then My thought are you may have a shorted wire. The turn signal flasher works by heat build up within the flasher the heat is caused by the load of the bulbs, the load heats the metal spring causing it to open the circuit then as quickly as it cools down the circuit closes again lighting the bulbs.
There is also a possibility of a defect in the turn signal mechanism on the steering column. The turn signal switch on many models does three different things on many models that use the same bulb element / or bulb for brake and turn on rear of vehicle. It controls the circuit for brake light by sending power both left and right side rear when turn signal is in neutral position then when turn signal is in left turn the switch cancels brake light power to left side rear and supplies flasher power to left side while maintaining brake light supply to the right side rear, and so on opposite when the right turn is chosen on turn signal switch. The turn signal indicators on the dash normally run off the same circuit as front turn signal bulb only which is also controlled by turn signal switch. Front has turn signals but no brake light.
I think there is an additional load on the left side rear turn circuit and it could be either a wire that is shorted or the turn signal switch if the same bulb element is used for both functions.
Often times if trailer lighting is connected the flasher will also blink a little faster because of the extra load of additional bulbs.

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 fast blinking is usually a bulb burned out. Replace the rear bulbs. If this is not the problem , it may be a ground issue, but it really does sound like a bulb issue. Also inspect the light socket while you are there. Look for any bad corrosion Good luck

Replace the turn signal switch. Bad contact inside causing a crossing of the circuits. When the turn signal is applied it should open the brake light circuit allowing for just the signal to work. Doesn't sound like the switch is doing it's job.

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

No, but that's probably where your problem is. The wires get the hell beat out of them by stones, and then they short out and cause problems. I would take a look at it.

Sounds to me like a bad ground. When the current can't complete through a ground circit it feeds back through the elements ancd can cause all sorts of wierd syptoms.

The fast blink itself can be casued by a burnt out bulb I would check that first.

Then I would check the trailter harness if there is one and unpluch any harness that may be plugged into it. also check each bulb to see if it is seated well. you may be able to see if there is corrorsionaround the bulb terminals at this time is so yo may need to replace the light assembly. Also you could look for any spot where maybe someone in the past tried to tie into the harness to hook up additional lights etc. this may allo moisture in and corroded to the point the wire is "open"

It sounds like a wiring fault - an earthing problem. Have a look around the lights/inside the lights themselves.. rear and front lights, brake lights, etc ...check the wires for corrosion/splitting. In particular check any black earth leads where they attach to an earthing point.

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.