Wow! I find this thread when I am looking at the same problem and have gone through many of the same checks as jkycjks. My problem is on a GL1800, but surprisingly, most of the components are the same. I believe the main difference is that the GL1500 asks the rider to toggle the bike in and out of reverse, where the GL1800 users the reverse shift actuator.
The symptoms are that the bike will not run in reverse and the reverse light blinks when you press the reverse button. When the bike is not running, but the ignition is on, the reverse actuator "activates" ( you can hear it ) and the light comes on as normal. But when the bike is running reverse does not work.
Basically, here is what I have checked out.
Fuses (#9, #10, #23, and the Speed Limiter Fuse) = good
Reverse actuator and reverse shift relays = functional and works correctly
All relays check out including the two power control relays and the speed limiter relay.
The reverse position switch ( the one on the reserve shift actuator ) and the reverse switch ( the one on the side behind the motor ) check out.
The reverse resistor assembly checked out. I also swapped out the reverse control module with another bike and the reverse control module does not appear to be bad.
So why doesn't the reverse activate. Well, for right not, I am not sure and I am still testing the problem. One interesting thing that I noted from jkycjks's post is the following quote.
Tonight, I checked the Starter Relay Regulator:
the LT BLU+ & GRN- ~1 V when pushed the starter/reverse switch;
the LT BRN/RED+ & GRN- ~12 V when pushed the starter/reverse switch after 0.3 seconds, think it's right cause it's over the minimum 4V;
Basically, I think this parts working normal and pass.
See, I have the same voltage on that side of the starter relay switch A. Actually, the relay reads battery voltage on that leg. The problem is that it reads battery voltage on BOTH sides of the relay solenoid and so, therefore, there is not current going through the solenoid and it does not active. jkycjks, measure both sides of the coil. Make sure that the voltage is not the same on both sides. The yellow/red lead should read battery voltage and the brown/red line should read less than battery voltage. I have checked working bikes and the voltage seems to be around 10-11 volts. This is where the manual is wrong. The minimum voltage may be 4 volts, but the maximum needs to be less than Vbat - or else current does not flow across the solenoid.
My reverse will work if I place 12v across this solenoid. So I am down to the reverse regulator assembly, but, after reading the posts here, I will check the starter switch before I replace the regulator. While I can't figure out how the switch could do this ( as the bike STARTS fine ), I have never ruled out the switch in my mind as it is a likely culprit.
If there are any other ideas I would love to consider them and I will post the results of the test I do tomorrow.