Inside the driver side front fender, it should be located near the brake system.
Check under the battery tray.
That would be a vacuum reservoir.
According to my owners manual for my 5 speed 1999 S10 it's 18.5 gallons (70.0L) standard tank.
It is located inside the fuel tank.
You have to remove the filler neck and hose from the tank then slip a siphon hose into the tank.
It is a vacuum reservoir to keep the HVAC controls in operation when engine is not producing good vacuum such as under acceleration or climbing long grades. Newer S10's still have one but it is hidden inside the drivers front fender.
Most likely in the fuel tank.
Remove the fuel tank or remove the bed, your choice.
It is in the tank. You need to remove the fuel tank to make this replacement.
Test it with a vacuum gauge.
Sounds to me you have a vacuum leak. Check under the hood for a unplugged or broken vacuum line. I think that model has a vacuum reservoir attached to the under side of the hood on the drivers side. I have seen that vacuum line pulled off accidently.
you have to remove tank