It is attached to the starter.
YES.
The starter solenoid is attached to the starter.
There is no 2001 S10 with a V4 engine.
Follow the positive battery cable from the battery, it will lead you right to the starter.
On the passenger side of the engine in the back.
Should be on top of the starter - follow the + battery cable
Backside, lower, passenger side of engine.
Well, honey, the starter on a '98 Chevy S10 is located on the passenger side of the engine, towards the bottom. You'll have to crawl under there like you're hunting for buried treasure to get to it. Just make sure you disconnect the battery first, unless you're looking for a shocking experience!
Inside the fuel tank
In the fuel tank
It is attached to the starter, just follow the positive battery cable from the battery, it will lead you to the starter solenoid.