Hey Spotty ...what a great solo it is to (I learnt it a while back and love playing it in the middle a jump blues song or something...)
there's a few old gibson and gretsch amps available I think but to be honest I think it's probably the guitar and the actual playing style that make the sound more than the amp ..try a fender or something and pick a little closer to the bridge ?
Have fun learning
Agreed with the above. The biggest component of the solo tone is a true hollowbody guitar (you can hear it in the thunk in the low notes and the attack on the other notes). If your Gibson type guitars have hot pickups, I don't think you can get really close to that cleanliness in the tone.
There's also a few Silvertone amp profiles on Rig Exchange that might get close if you can get them clean enough, as well as a bunch of tweed Fender amps. But the big secret is in the hollow body of the guitar.