I have a 1990 HDJ80R and I have a starting issue, when I turn the key it takes about 2-4 seconds after I've turned it to start.
It's only just started to do it on and off.
Would it be the starter relay on the left hand/passenger side guard in the middle?
Start by making certain both batteries are fully charged. Clean the battery posts and make sure they are "tightly clamped"
The above is simple and my son who is in Whistler actually figured this out.( little help from the old man via phone)
There should be a wire from starter solenoid to a connector...try taking apart and cleaning, this sometimes has crud.
Another spot is the fusible link. The fusible may test OK with a test light, but is not capable of taking the full load.
I have also added a momentary switch under the hood which allows starting via 12 volts as an emergency option.