Don't believe a thing you see in a video, yeah Iha is using a jazzmaster, whether it was used in the recording is another thing.
The only time i've seen Billy Corgan with a mustang is in an old clip from the 80's when he was in The Marked, never while he was in the pumpkins, he might have used one, who knows?
Corgan used Strats with lace sensors through the Mellon collie tour running them through a JMP-1 preamp, a mesa boogie strategy 500 power amp, an eventide H3000 and a bunch of pedals including the purple Boss flanger (as seen on LOVE) and a Digitech Whammy (as seen on X.Y.U).
You'll have a tough time getting the exact sound you want, but a strat with sensors and the same pre and power amp running through a mesa 4x12 will get you 90% there.