There’s always been a question as to what gear Clapton used on the song, and none of the people at the session can remember exactly, so this answer is lost.
Here’s what Ken Scott (who engineered the session) said in the book he and Bobby Owsinski wrote together Abbey Road To Ziggy Stardust:
“The “While My Guitar Gently Weeps” sessions I’d really like to remember since I’ve been repeatedly asked about them, especially the Eric Clapton overdub session, but the only recollection I have is of mixing the song. Eric had been reluctant to play on the record because “no one plays on Beatle records,” but was convinced by his good friend George that the rest of the band would be okay with it. To his credit, he wanted to sound as far away from Eric Clapton as he could, so he insisted on not using any of his own gear and used The Beatle’s gear already set up in the studio instead (I wish I could remember exactly what gear he used).
This wish to sound as un-Clapton-like as possible extended to mixing as well. In order to make it sound “more Beatley,” the ADT setup (see sidebar) was used to get the warbling sound that’s on the lead guitar and organ, since they were both on the same track. Chris Thomas was put in charge of manually turning the varispeed of the tape machine up and down during the mix to obtain the distinctive wobble.
“I thought it was stupid because it was such a gimmick, but that’s what they wanted because Eric didn’t want it sound like him. They wanted it really extreme so that’s what I did. I did that for hours. It was so bloody boring.” – Chris Thomas (George Martin’s assistant)