Check the diagram under the hood. You might have the belt routed the wrong way.
you have to determine which pulley it is. if the sweak is consistent, it could be the tensioner, water pump, well these are the first to go. the serpentine doesnt control timing. and loose is a possibiity.
The water pump mounted on the front of the engine, with a drive pulley attached to the pump hub. The serpentine belt usually drives the pulley.
On a 3.3l the water pump is driven by the serpentine belt. On a 3.0l the water pump is driven by the timing belt.
Behind the water pump pulley. The water pump is small so the water pump pulley covers the entire pump so you can't see it. Once you remove the serpentine belt and the water pump pulley, the pump is easily accessible.
On my '92 it is below and behind (towards the back of the engine) the water pump. It can be easily recognized on most cars because it's only pulley that rolls on the BACK of the serpentine belt; a BRILLIANT idea if you ask me.
Replacing the water pump and belt should not affect turn signal operation.
The water pump would be a standard rotation. The serpentine belt moves clockwise on the model truck which would make it standard not reverse. With a serpentine belt system like the one in the 2000 S10 4.3, any pulley that is grooved turns clockwise. Any pulley that is smooth turns counterclockwise. The water pump pulley on that S10 is smooth and turns CCW.
It goes underneath the water pump and around the next pulley.
Rear most and lowest pulley on the serpentine belt.
if replacing the battery doesnt fix it.
The water pump on this model is located on the top of the engine to the side with the serpentine belt. Its pulley will be the one with the smooth wheel
should be a sticker on fan shroud Alternator, idler pulley, power steering, a/c, tensioner pulley, crankshaft pulley, water pump this is the order cant upload the picture but when placing the belt on if the pulley has the grooves in it the grooved side of the belt should face the pulley and if the pulley is smooth then the back of the belt faces the pulley