If it's blinking, it's a turn signal.
Your taillight is burned out.
For the front turn signal on a Chevy S-10 you remove the parking lamp lenses and replace the bulbs. If it is a rear turn signal bulb the taillight lenses will have to be removed to access the bulb.
Replace the bulb, it has two filiments/ One for the tail, one for the turn.
Turn signal indicators are lights. The flash to tell you, or indicate, that a turn signal is on, and which way the lights are flashing.
On the left side you have to remove the auxiliary battery control panel face plate to access the three bulb system of taillight, brakelight, and turn signal.
The yellow light bulb indicates that there is a blown bulb ( taillight, turn signal, etc.) somewhere on the vehicle.
You have a ground issue. More than likely it is not grounded properly. These can be very, very, hard to find. Been there and done that. I can only tell you to check all ground connections at the taillight assembly.
rear you use a torx driver to remove taillight assembly screws. them replace bulb.
the turn signals will not work
Open The Rear Hatch, pull off the taillight lens, locate the bulb, Push the bulb in and turn at the same time. It Should Come out.
Open hatch. Theres an access hole inside towards taillight. Unscrew plastic knob by hand. Along side of taillight -(outside of car)- in the drip rail- there is a Philips head screw. Undo this and pop taillight assembly out. Turn bulb holder to remove. Reverse process to install
If the turn signal relay & hazard (emergency) relay are side by side, turn on the emergency blinkers. You will hear & feel (if you touch the relay) the emergency relay clicking. Turn signal relay is the other one.