Is there any type of pen that would be able to stay on a black les paul pickguard? (It's kind of glossy plastic)? Or would my best bet be to buy a diff color/type of les paul pickguard?
Metallic Silver Sharpie.
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you could get it signed and then sprasy a few coats of clear paint on it i think.
Clear Paint /Varnish over it might work, or it might smudge it, Silver Sharpie in my opinion.
I agree with these guys, silver sharpie.

Let the ink dry for a few days (just to make sure it wont smudge) and then spray some clear paint over it
i had my paintball gun signed by ollie lang (it's metal) and it was black with a silver sharpie and i clearcoated it a day later, it looks good that was about 6 months ago and it's still there i think i did abot 12 coats of just regular colorpalace sprayon clear, it didnt smudge.