98 S-10 pickup LS extend cab. Rear left turn sig. and brake light not working. Front left blinks faster then normal. Replaced rear left turn/brake bulb twice. Right side front and back, turn are working normally. Right brake light also works as it should.

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

indicates a problem in the harness to the rear harness
cut wires , incorrect additions to harness
possibly along the chassis or under body

turn on park lights and signal on right side and take a good look at the front and rear light , see if one is dimmer than the other this may be due to a bad ground and when the park lights are on and drawing more power it also needs better ground, check the sockets front and rear try wiggling the bulb to see which one is causing the problem

Turn Signal Lamps
The LT T/SIG and RT T/SIG fuses located in the underhood fuse block supplies battery positive voltage to the body control module (BCM) for turn signal and hazard lamp operation. When the turn signal switch is place in either the LEFT or RIGHT position, ground from G202 is applied through the turn signal switch signal circuit to the BCM indicating the turn signal request. In response to this signal, the BCM applies a pulsating voltage to the front and rear turn signal lamps supply voltage circuits cycling the lamps ON and OFF. The BCM also sends a message via GMLAN to the instrument panel cluster (IPC) to cycle the turn signal indicator ON and OFF depending on the position of the turn signal switch.
Ground for the turn signal lamps is supplied as follows:
• G101 provides ground for the left front turn signal lamp
• G100 provides ground for the right front turn signal lamp
• G302 provides ground for the left and right rear turn signal lamps

The LT T/SIG and RT T/SIG fuses located in the underhood fuse block are also used by the body control module (BCM) for stop lamp operation.
The brake pedal position sensor is used to sense the action of the driver application of the brake pedal. The body control module (BCM) provides both, a 5-volt reference voltage and low reference to the brake pedal position sensor. The position sensor provides an analog voltage signal back to the BCM that will increase as the brake pedal is applied. When the brake pedal is applied, the BCM will then apply battery voltage to the left and right stop lamp supply voltage circuits and the center high mounted stop lamp (CHMSL) supply voltage circuit illuminating the stop lamps. At the same time the BCM signals the transmission control module (TCM) and the engine control module (ECM) that the brakes are applied. Ground for all stop lamps is provided at G302.
The stop lamps on this vehicle will not illuminate unless the ignition is in the accessory, run, or crank positions. When the ignition is in the OFF position the stop lamps will not illuminate when the brake pedal is applied.

Did you check the fuse's. ? Wouldn't think it's a ground because right an left tail lamp Assembly's use same ground ! Did you check for B+ voltage at the bulb. with a volt meter ? Power is supplied by the BCM . Could be the tail lamp assembly

Normally with the blinker blinking really fast, it's telling you that one of the bulb is blown, front or rear signals. Check your fuse, and fuse relay to see if it would fix the promblem

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.

check and replace the bulb in the rear left light, the fast blink is normal when the front or rear bulb is out, the brake light not working indicates which one is out

sounds like the bulb you have is the wrong resistance the new noen bulbs will do this