Brian, it comes on for about 3 seconds once you turn the switch on like the oil light and a couple others. It will go out whether or not you start the engine. If it's on the engine won't start because the starter will be locked out. I believe the source of your problem is either the reverse switch down by the reverse handle not operating or possibly the reverse relay hanging up.My GL 1500 is in the shop so I can't test this at the moment...
Does anyone remember: Does the Reverse light come on at start up? Also, does it stay on until the engine turns over and runs?
Thanks.... Brian