There are common known (and some little-known) issues with the GL1000 charging system. First is that the alternator is permanent magnet, so it always puts out power primarily proportional to the speed it is turning - there is no field coil to regulate. Because of this, the regulator grounds any excess power to keep system voltage in check. Next, on Euro-spec models, one phase of the alternator poers the headlight, which can be switched off. To allow for this by simply changing the handlebar harness, Honda runs one phase through the main harness and just puts a jumper in the NA spec handlebar harness. Extra wire and connectors that can be bypassed here. Another weakness is the "three yellow wires" connector between the alternator and harness often fried, invariably heat darkened, and too often the cause of failed stators due to phases shorting out in melted connectors. To add to this connectors harsh life handling full load whether needed or not, it is located near the old battery vent tube (please, go to a sealed battery) where acid fumes make life even worse for it. Then the three phases (with one taking the scenic route to the front of the bike and back) go through another connector to the rectifier. This connector is also located in the vicinity of the battery vent. On many old wings, you will note the greater amount of corrosion on the front part of the battery frame. Close to the vent.
I have learned to remove each of these connectors by first drawing well notated sketches of each plug, removing the connector pins and sockets (there is a tool Lisle 14900 for that), clean them if good, replace if not, and make sure crimping is done with the proper tool. Pins sockets, connector bodies are all available very reasonably from Vintage Connections, as well as good crimpers. All of this is done much easier withe the harness laid out, off the bike. Great to pass time while waiting for parts, paint to dry, etc.
Most replace the three-pin (three yellow wires) connector by either good soldered and heat shrinked connections or some other improvemen. I'm using 50 amp gold-plated RC helicopter connectors soldered to the wires and heat shrinked over. So far successful, but with only a couple years in service.