When my engine is under a load(going up a small hill) the battery light comes on until the engine is not under a load. I've checked both the battery and the alternator and they are good. I've tried putting the engine under a load in my driveway up to 2500 rpm but the light didn't come on.

You should get a full charging system test. It'* likely there could be something wrong with it, and load is pulling it below threshold enough to trip the light.

"not under a load" as in coasting down the other side of the hill or as in still under a little load on level road?

When safety allows: Can you try causing this behavior again, then let off the gas gradually while still going up the hill and note what speed the light goes out?

Checked with a load tester or a volt meter?

What RPM is your engine at when going up a small hill then the light does light up?

I'm thinking maybe the regulator could be going bad in the alternator but doesn't show itself until xRPM . . . ?

I take it, you don't have a voltage gage?

Attach a voltmeter to your battery, and lay it under a wiper blade as you drive.....note the voltage when the light comes on....