I cannot watch the video here
in work on my lunch break.
From memory, didn't Chris have the pickup re-magnetised at some point and found it was too strong? I recall reading that the bridge pickup on his bass was disconnected, quite purposefully, though some took this to mean that he never used a bridge pickup while others claim that it was only done temporarily when the pickup was too far degaussed to be useable. There is also the fan theory that his original bass had the bass-cut cap removed in the early '90s at least for a short spell. I saw this theory fleshed out on the YesFans page (I think) or possibly on here.
I enjoyed, and was frustrated by, the Chris Squire rig rundown video in equal measure when it came out. He either had the civil servant skill of saying a lot while saying little, and keeping some tone secrets to himself, or he was maybe not the gearhound that some of his fans are. The heart of his rig seems to be an old Rickenbacker and some old Marshall amps. His bass ran in stereo but somewhere was mixed back to mono before hitting the Marshalls, which were used basically to fortify the signal before it hit other amps in turn. He used a few battered old effects pedals, some of which were in the stereo setup at least. Some of his signal chain seems unchanged from the Syn days, and given his state of confusion about the extra pickup on his Jazz bass (where he must be thinking of his Telecaster bass) perhaps he really wasn't hiding anything.