Can anyone tell me how the electronic speedo and the also electronic trip speedo works in the center dash panel of the 87 GTA?

 

The speedo head receives the current pulses from the VSS. Inside the speedo is a two-pole permanent magnet "motor" that converts the pulses to motion (much like a regular induction motor). This "motor" drives a magnetic coupling against a spring. The magnetic coupling is connected to the speedometer indicating pointer (the one that you see). The motor also drives the odometer, whose digits are stepped by the rotation and a ratchet/pawl mechanism. The trip odometer is simply mechanically linked to the cumulative odometer. This is why the electric speedometer and odometer will display speed and accumulate mileage in either direction (forward and reverse).