Why not on a Tele!? I don't know for sure what Mark then had on the two Teles they had. I very much love the sound of probably the sunburst Tele on Dylan's Slow Train Coming, e.g. on Precious Angel or I believe in you, might be the 008, too, with a brass Schecter bridge. Maybe he even had thin strings on the black Tele, why else tuning it to open A instead of the more common open G (which he also used on his National)?
Hendrix was also known for a 038 low e string (010-038) so...