Only when the vehicle(97 SSE) is running, I get a high pitched whir/whine coming from the back of the vehicle. Not a tire or anything, as it is only when running.

Exhaust or line, or what?

Can you tell about where the sound is coming from? The ELC pump is right behind the right rear tire.

Yes, it is louder on the right rear than the left rear.

The only other thing back there is the fuel pump, which can make a noise like you describe. Does it happen all the time the vehicle is running, or does it cycle on and off?

That'* another possibility, but he can poke his head under there and peak. If it'* the compressor, you will see it right there. If it'* not coming from the compressor then the fuel pump could be it.

Just replaced fuel pump in December.
Just started happening today.

And you didn't answer any relevant questions. Is the noise steady, or does it cycle? Is it a high pitched whine, or does it sound like a small air compressor running?

EDIT: Also, is your power antenna in the rear working as it should too?

Sorry about that, sent that post very quickly, had some things going on.

The noise stays steady. Sounds like a small air compressor.
The noise was there for about an hour. Turned off and on, noise would come back.
After sitting for 3 hours, I started her again, no noise, and drove for about 3 hours and got no noise while driving or while stopped.

Also, no the power antenna doesn't work; however, I don't have a motor on it right now; since it doesn't work, replacing it and just took the motor off.

The compressor is on a timer circuit and can't run for more than 10 minutes. Like mentioned, it would be your fuel pump or the antenna. You took the antenna out of the equation.

The reason it quieted down is you probably filled the gas tank.

I didn't add any gas or even park on a different elevation.
Would the fuel pump really give out after just a few months?