Need some help with simple electrical issue!

pjbgravely said:

The top prong as 5.1 volts either looks like the BCM is controlling through the ground side and is dimming the bulb. If that is not the case then then you have a bad  ground.  Make sure your measurements are done with the bulb in the circuit. Perhaps draw the circuit out and show where you are getting the measurements. You will probably understand more when you do this.

Getting a wiring diagram is the best way to diagnose electrical problems.

Oooh, I didn't know I needed to have the bulb in place to check for resistence.  Why is that?  Do I also need it in there when checking voltage?

You need the bulb it in place to check voltage under load.  What are you checking the resistance of? You can check to see if the bulb is good, and check that you have a good ground, but other than checking both ends of the same wire it isn't going to tell you much.