The tap dancer who Derek Bailey peformed with was Will Gaines. There is an album called Rappin' and Tappin' on Incus, reviewed like this by Volcanic Tongue:
Will Gaines & Derek Bailey
Rappin & Tappin
Incus CD55
Rappin & Tappin is an inspired and rewarding set, joining the dots between two improvising talents who manoeuvred their way to freedom from the heart of dancebands (Gaines was a member of Cab Calloway’s Cotton Club Revue and opened for people like Eartha Kitt, Nat ‘King’ Cole and Sammy Davis Jr) and further expanding Bailey’s radical concept of totally free improvisation by way of his sonic responses to the unlikely raw material of Gaines’s percussive codes. The first few tracks feature Gaines alone, moving from bombastic two-foot build-ups that almost sound progressive to beating out trap patterns straight out of Art Blakey’s songbook. Alongside the tapping, Gaines reminisces about his time working with various jazz musicians in clubs and the combination of rhythm demonstrations and oral testimony means this part of the disc lines up nicely with Baby Dodds’ Talking And Drum Solos set. However, it’s the second half of this live recording that’s the real gravy, with Bailey playing an amplified acoustic with a pedal, accompanying Gaines’ dancing with warped metal wows, ramping chords and delicate – almost swinging – patterns. It’s always weirdly illuminating to hear Bailey working with a percussionist who plays time, and there are points here where Gaines’ footsteps sounds like Han Bennink’s floor work, while at others it sounds most like the rain on Bailey and Min Tanaka’s great Music And Dance recording. Either way, this is a consistent dazzler.
(I've edited this because I think the Volcanic Tongue review is better than the one from The Guardian that I originally posted)
There is apparently footage of the two of them
HERE. I say apparently because there is a firewall between me and the relevant site.