Dome Light And Defogger Not Working

I believe you may have two separate problems. If the light on the defrost switch does light up when pressed this "proves" that power is going to the defroster from the relay. Check there is power, ground, and continuity at the defroster grid itself.

Does the dome light work if the head light switch is turned all the way until the click that turns on the dome light?

The GEM is grounded at the same body point as the radio is. The ground is not just a single wire but a collection of black wires coming together at the same point. The GEM ground is frequently messed up during a radio install.

If this were my car I would confirm the GEM ground all the way back to battery negative. Here's some information on one method to test using voltage drop. Another method is to use a test light with the lead on battery positive. Test the black wires at the GEM itself.

The testing methods also apply to the defroster grid testing.

Howto perform charging system voltage drop test
https://www.stangnet.com/mustang-fo...perform-charging-system-voltage-drop-test.56/

It also seems to me that a full set of Ford wiring diagrams is what you need. If interested in getting a set for yourself I maybe able to help. PM if interested,

PS the wiring diagrams in the Haynes manual are rarely complete. Only really good to give an over view of the circuit. Use the Factory diagrams and you won't be disappointed. It will save you a TON of time trouble shooting an electrical problem.