Currently having an issue with my speedometer bouncing for a bit and then not reading anything. Soon after the ABS light comes on, but the truck continues running fine. When I restart the truck, it works fine again until 10-15 minutes of driving, then the same problem again. I have a 1996 F150 XLT RWD 4.9L standard if any of that matters.

 

What ABS code(s) did you get?

 

Your ABS lamp on, and the speedo bouncing are likely two different problems.
You need to look and see if you have 4 wheel ABS or RABS (most likely RABS on your 1996)
You ground the wire for RABS and count the flashout code
Rear axle speed sensor output millivolts check (the faster you go, the more volts it puts out), needs to be smooth, up and down with speed
Don't get a cheap VSS, get a Motorcraft one with the ridges
check the connector wires, they like to break off at the rear axle sensor
RABS valve failure (coil resistance out of spec) is the most common problem with RABS IMO (that and the brake pedal dropping)

 

A 1996 model year F-series trucks uses the Rear-wheel ABS (RABS) system.

Here is the procedure and decoder for how to pull the RABS Codes

 

You could be correct but the same signal from the VSS feeds both the ABS and the speedometer so how can you make that assumption at this point?

How do you know the sensor is bad and not a wiring problem?