I watched Gimme Shelter again the other night, and I noticed that in some of the footage, Keith is playing a sunburst Bigsby-equipped Les Paul. Is this the same Les Paul that Keith used in the early days? The Sullivan clip and the film of "Around and Around" come to mind. Was this one of the guitars stolen from Nellcote?

It was up for auction a couple of years ago, so it can't have been stolen at Nellcote
check this thread: [iorr.org]

The sunburst-Bigsby-Les Paul was sold, to all people, Mick Taylor
while he was with John Mayall. It was either sold or probably stolen
a few years later (why would one sell THAT guitar, but you never know).
I do remember it on auction a few years ago. Did it have a certificate of auth?
I can't remember.

The guitar was up for the sale by Rock Star Guitars two years ago and was soldf or about $400,000 if I remember rightly but then it came up for auction last year at Christies but didn't sell. The guy who has it now doesn't even play, he just bought it as an investment. To answer you question Wattsfan I do believe Tomk is correct in what he says.

I always had a feeling that Taylor got the gig 'cause of this guitar.
Although it was Keith's guitar, Taylor said he got it from Ian Stewart
who was acting, I guess, as a go-for in this situation.
Stewart alwyays said that Taylor was his idea to replace Brian.
Perhaps he remembered him when Taylor was trying out this guitar.
Or maybe he saw him with Mayall. But it seems like Stu wasn't
a club-concert going guy, so who knows. Just a thought.
(and don't respond with "i'm glad it was just a thought, tomk")