There are a few photos of Jimi playing a Fender Jaguar (see comments) in what appears to be either a dark blue or black finish. All of the photos seem to have been taken on the same day. August 24, 1967, at Lime Grove Studios for the Top of the Pops TV show.
The most intriguing detail about the guitar is that it was strung for a right-handed player, suggesting that it likely didn’t belong to Jimi and was borrowed just for that occasion. Beyond this, the guitar remains a mystery. If you happen to find any mentions of it by Jimi or someone close to him, feel free to leave a comment.
Ike Willis from Frank Zappa’s band said that Jimi gave Frank a blue Jaguar, and Frank let him play it during his first tour in 1978. Maybe this is the same guitar.
Your link is broken now, but here are a few pictures of him with the Jaguar: #1, #2, #3, #4, and #5 which seems to possibly verify that it was indeed blue. Of note: his clothing remains in the same in all of the pictures I found of him with this guitar (which are the five included here… I didn’t find any others), so to my knowledge, too, no others exist outside of the TOPS recording.
The guitar wasn’t even plugged in so maybe just a photo shoot or back-up video? I think he played live with his strat on Top of the Pops