I agree with Artie: it's most likely a "safety cap" from ground to stop bar. My friend luthier mounted such things in his guitars too.
Tonally, it's not doing anything, like beaubrummels said.
And yes, a 500T effectively "sounds full and hot, just kinda fuzzy". Reasons: it's a high DCR/high inductance model with 3 ceramic mags...
Gibson tends to use 300k pots to tame it but it also makes it sound even fuller.
Pulling off the two lateral magnets and putting a single AlNiCo magnet in center position would calm it to some extent.
Now, let's share is a possible trick to make it less hot AND brighter sounding without modifying it. It's an extrapolation on the old Bill Lawrence Q filter principle, allowing to use a choke (an inductor) to revoice a pickup...
-find some cheapo 16k MIC humbucker. it costs a few bucks on various sites. A model with two rows of slugs would work well.
-pull off its magnet and baseplate. Just keep the coils and their wire. You have now your choke / inductor (and you could even use it to build a VariTone by adding some capacitors on a rotary switch to it).
-connect these two coils and nothing else in parallel with the 500T. Leave them in the guitar. There's normally enough space in the electronic cavity for that. Just avoid the thing to touch any hot wire (insulating tape is your friend there).
It will divide by 4 the sum of the DCR and inductance of both pickups, without added noise. As the 500T is hot as heck, it won't be annoyed by an inert pickup in parallel. It will just sound closer to a P.A.F. replica, with realistic resistive / inductive values (around 8k and a bit below 4H, most likely).
I share this idea because I've already applied it and know that it works as long as proper components are used (500k pots welcome in this case, BTW). FWIW. HTH...