Hmm, SteveAJones. Interestingly enough, it's also been said he went off then to see a girlfriend in Los Angeles. Also, it's well known that there was a connection between the band Love (Hendrix had actually played with Arthur Lee in 65) and there is no denying that some VERY Yardbirds guitar statements ended up on "FOrever Changes", which still stands as one of the greatest records ever made, recorded just a few months after Beck left the Yardbirds.
I have heard/read that Beck was in LA hanging out with members of Love after he quit the Yardbirds, also that he had hung out with them on earlier tours. Hendrix had actually recorded some tracks with Arthur Lee, and the British guitarists were equally attracted to the guy (Lee) pretty much universally recognized as the best rock singer in the world. They all wanted to play with Arthur Lee.
This particular Love record, which ended up being Forever Changes, was a big in deal in the music industry, which, as all the bands in California and the Yardbirds figured out eventually, didn't quite yet have its Woodstock hardon. In any case, this Love record was considered a big deal -- initially, Neil Young was signed on to be the producer of the record, and Jack Niietschke was also involved. In the end, they didn't do the record -- Bruce Botnik, the DOORS producer, made the record. It's fuckin brilliant.
So what does that have to do with Beck and Page? Well Track 2 on Forever Changes, "A House is Not a Home" is nearly verbatim the guitar solo on "Happenings Ten Years Time Ago" - which is on the Roger the Engineer record the Yardbirds were touring at the time.
I'm going to argue that Beck played that solo, though it is uncredited. I'm also going to argue that Beck's idea was that he and Jimmy should go to LA and play with Arthur Lee, hence the well-reknowned story, "I'm leaving ... you coming???" -- to which Jimmy said, No.
EDIT: I'd have left with Jeff to play with Arthur Lee. Keith Relf had become horrible. He wasn't even any good any more but for his harp playing, which was always great, though it ruined the middle sections of the "Dazed and Confused" Jimmy was trying to do later on after Jeff quit. Anyway, Relf was not delivering.
I'm listening to Forever Changes right now, an album that was never played out, never toured, and the only reason most people know about it is that THe Damned covered 'Alone Again Or' -- With Jimmy and JEff, Arthur Lee would have conquered the world, and I have no doubt that was an idea that Jeff wanted to actualize. Really, at the time, 1966, everybody wanted to play with Arthur Lee.
I think the Yardbirds guitarists were all over it - Hendrix was already gone to England.