FWIIW, 5 Ohms is a lot of resistance for what should be a straight wire.
Also, the dome light ground goes through the GEM. Guess where the GEM is grounded? If you said G203, give yourself a gold star.
The circuit is actually very simple. The diagrams attached.
Did you confirm there is +12 volts going INTO the fuse?
If the fuse is good, then you should be able to test +12 volts to the outlet center and a known good ground. If no voltage, then either the fuse is blown, there is a wiring fault, the outlet itself is burned out, or your tester is bad.
2003 GT Convertible (sold & missed)
2000 GT coupe (Craigslist project. Fixed. Now my DD). Windsor to Romeo swap.