In his 1999 Tokyo Concert DVD, he straps on a Fender JB Strat with the skinny Lace ball-bearing nut for a few bars of (as I recall) Blue Wind, probably just to fulfill contract obligations, and then it's back to his #1 mutt-strat for the rest of the show.
There is also a black 87 Strat Plus on Ebay with the original 1 st generation Wilkinson nut on a rosewood board and having 3 s/c Lace sensors .
So,my comment about 'searching in vain' for such a guitar was overstated.
Jeff Beck doesn't play a Jeff Beck Strat. You'll search in vain for an early JB Strat or Strat Plus with that 1st generation Wilkinson roller nut, and you can't buy one to install as they aren't made anymore. Just buy a early 90's Strat Plus w/ rosewood board and having the 2nd generation Wilkinson roller nut which has all 6 strings running though it. Then, install good quality single coils in place of the Lace Sensors. That's about as close as you will get to the guitar Jeff's been playing for over 20 years.