I've been having problems with my right side losing power, and for a while I've been able to subdue the symptoms by jiggling the spark plug cable. Well that doesn't seem to work any more. So I unscrewed the spark plug cap assembly, and the screw in the cap is bright, but the cable is all gunked up on the inside so I figure this is probably the problem.

I've tried squirting it with cleaner, but that didn't seem to budge anything.

I was thinking I could snip an inch off the end of the spark plug cable. Is this a good idea?

The GS does not have a cable that screws into the cap (this I am not sure) nor does it screw into the coil - This I know for sure.
If your problem is in the plug side, you could cut the cable a wee short and put a unscrewable cap if the cap is not unscrewable kind.
If it is on the coil you would need to replace it with one that has the same impedance range.
Cool.
Buddha.

This is what I'm working with (pic below). So you're saying I can just clip the tip of the cable?

http://imgur.com/a/z8Mekof

Anyway, I snipped about an inch off the spark cable and nothing happened, but when I nudged the wire that goes INTO the coil, the bike started working again.

So your issue is at the coil end. That part is glued in isn't it. See what it looks like under that glue etc. You may need to get the whole coil swapped out of a bike that has a screw in end at the coil.

Cool.
Buddha.

It's not the spark plug cable it's the other wire that goes into the coil. I'm going to replace everything in that area in a short time, just need to get the money together, but now I've finally figured out exactly what has been plaguing me for months.