To answer the question, yes I'm a fan of Pink Floyd -- everything up to The Final Cut, but their post-Waters records can't keep my attention. (Neither can Roger's post-Floyd records!)
Regarding Fat Old Sun, Gilmour certainly used his Tele for that in recent years - I thought it was a Tele on the original record but maybe not.
For some reason I thought it was a Tele. As someone else pointed out, Gilmourish.com lists all the gear for each album and he has it as a Strat.
It didn't make sense that the song is in the key of G but had an F chord (vs F#dim). I found out later that bands flat the 7 chord in rock.
Thanks for sharing the video. Never seen that before. I wonder why Nick Mason isn't playing drums..