Hi Zach,
The fuel pump would usually be fairly close to the fuel tank.
It could of course be anywhere between the tank and the engine,
but typically they are not made to suck, but to pressurise.
And if there is very little fuel in the tank,
one would still want the pump to deliver,
since it may not operate without any fuel in the pump,
then often the pump is near enough level with the base of the tank,
and close by.
Therefore even with only a small amount of fuel in the tank,
hopefully enough will enter the pump to allow it to deliver.
A pump in good condition will 'draw' fuel,
but may not work if it runs dry,
however even badly worn pumps will usually operate when primed.
The rough and spiky nature of vehicle electrics can be disastrous to
home-made electronic stuff unless it is taken into account.
And the battery could be anywhere from zero to fourteen volts,
this alone can be a problem for some circuits.
When 'jump-starting' a vehicle using a battery on another vehicle
there are many stories of charging systems giving problems afterwards.
My own routine when i have to 'jump-start' is as follows, born of many
painful breakdowns, i follow it carefully, and have had no problems
using it, or after using it, with either vehicle.
* both vehicles off.
* attach leads.
* start the host vehicle (the one that will run)
* let it run for a few minutes if possible (to put some charge into the client)
* attempt to start the client vehicle.
* If possible turn both off to remove leads, otherwise turn off host.
I feel this routine has on many occasions saved me problems,
which would previously have given me at least one or two further
problems with the charging systems.
Sorry i'm not familiar with a Chevrolet S 10
maybe someone will drop in with that info ...
Best of luck with it, John