Looking at a wiring diagram, the parking light and speedometer internal lighting share a common wire a green wire with a black spiral band, it's the 12 vdc power for these circuits .
Looking a bit farther back on the wiring diagram, this wire comes straight from a fuse .
You may want to check the fuses for corrosion, or security, or broken, frayed wire at the fuse holder, this fuse box is a known area for causing problems !!!!
Suggestion, replace the fuse box with automotive blade type fuses when you can get around to it .
If the fuses are good, there is a splice where both of the lights share a common place, that could fail .
But at this splice the other wire goes off to the tachometer, for internal illumination .
If the tachometer lighting is working, most likely there is a problem with this splice .
I'm sure it's buried in the harness, with 33 year old cloth tape on it .
With your current situation with a fairing, it's going to be a bit of work to find out what may be wrong with the wires .
As far as grounds are concerned, the parking light shares the same brown ground wire as the head light bulb .
A problem here would either cause just the parking light not to work, or have a problem with the head light as well .
The ground for the speedometer light circuit goes straight to a common ground splice that all the circuits in the instrument cluster, front turn signals and head light parking light share .
A problem with this ground would only cause the speedometer light not to work .