Thanks for your help. I got the new switch installed. I was in a bit of a hurry, but did spot checks of the circuit against the diagram, and it seemed OK. But, after putting it all back together, it still is not correct. The positions play as described before. However, there is now the additional position of "middle" for the pu switch, with the result of now both pickups are in play to some extent with the phase switch down, but only the neck pickup is in play with the phase switch up.
There was a note inside the electronics bay, "Switch overhaul by Brian & Greg 2-18-86" so there was surely some mods done; the pickup switch was confirmed as a two position switch, not some failure of a three position switch. Brian and Greg also scratched their signatures inside the pickguard - Brian's full name appears to be Brian K. Ross, but Greg's was not discernible. There was also an inscription "89-79" with what looked to be initials next to it, but not sure what those were - most likely Brian and Greg's. The serial number of the bass indicates it is a '79 model. Would be nice if Brian or Greg were around to comment!
Anyway, I guess I have to make another try at this when I have more time. If wired correctly, then perhaps there is a bad capacitor, or other component.
I did take pictures of the electronics, so if anyone wants a look, I can send those.
Thanks for your help again!