OK...
It appears that there were a number of modifications to this board (that should have been implemented within the factory) described on
https://www.zimmers.net/anonftp/pub/cbm/schematics/computers/pet/univ/8032080-1.gif.
I can see some of the modifications on your board, but the UC3/3 to +5V track appears not to have been done for some reason.
It might be worth CHECKING these modifications against your board (to see which ones have been done and which ones not). However, DO NOT implement any that have NOT been performed.
As we almost had this machine working, then it is likely that what Commodore had done in the factory was fine.
With PETTESTER working (pulses on CPU pin 7 (SYNC)) can you check the following two pins on UC3:
UC3 pins 9 and 11 (/READ EVEN and /WRITE EVEN).
I suspect the pulses will be there - but you may have missed them last time around? With your new-found oscilloscope skills (sweeping the timebase) hopefully you may now see them? Report back.
Can you then move on to look at all the pins of UA2 (74166) - HIGH, LOW, or PULSE again. Don't forget to be patient and sweep the timebase if nothing appears to be on the pin. I have asked you for all of the pins on this IC. Some of the pins are connected to 0V and +5V (so will be a static HIGH or LOW). I will be using these as 'check signals' to see if your oscilloscope skills are improving!
We are on this schematic if you want to 'follow along':
https://www.zimmers.net/anonftp/pub/cbm/schematics/computers/pet/univ/8032081-08.gif.
Dave