Reverse gear will not engage on gl 1800 - 2005 Honda GL 1800 Gold Wing

There is a very sensitive adjustment to be made. Dealer work.

check the gear selector indicator for reverse, or that the loom hasnt got a wire unplugged at any point on the loom

It sounds like broken or stripped out gears in the reverse motor. You will need to remove it to check further.

turn on the ignition key, engage clutch and press the start button .
To reverse it put it on reverse and release the clutch slowly as when it is running

Pull out on the lever and push it toward the front of the bike, hard if necessary. Rock the bike while pushing. If the bike comes out of gear it should start. The bike will not start while the lever is up.
Probably need to replace the switch behind the lever. Don't test it, just replace it.

first place i would go is the switch either take it apart and clean it or replace it as this is what makes the reverse turn on this bike