Series/Parallel wiring issues...

I hate it when that happens LOL.

While the bridge is working (push/pull in up position), does the volume, blend, and tone control work properly on it?

 

I'm not sure your wiring diagram will do what you think it will. Series/parallel and blend pots can get complicated. Here are some threads to read:

Working blend pot with series/parallel switch?

jazz VBT with series/parallel switch

 

The diagram as drawn should work fine, so we are left to troubleshoot what may be miswired or other possible complications. Can you post a picture of your actual soldered connections? Do you have a multimeter to utilize to verify that connections are made? What pickups are you using? Do the pickups have any internal shielding or just standard traditional J pickups?
I assume you have the two jumpers making the “x” across the blend pot (red and blue in this picture)? When the bridge pickup is working does rolling the blend all the way to the neck side turn the bridge pickup off or is it still audible (in other words, does the blend essentially just act as another volume control for the bridge pickup or are there oddities with how it works?)? What are you using to make the “ground” connections (like the back of pots? And how are your pots themselves grounded?)?

Easy things to check are both the neck pickup lead connections, as well as checking that the switch is making the correct internal connections using your multimeter and isn’t damaged (cheaper push-pull switches are easy to overheat and damage )

 

If the red marker line on the diagram is a wire then it won't matter if you connect the ground to the top left or the bottom right.

 

I'll assume for the moment that if the bridge pu is only working when push/pull is up, that the controls (Master Vol, 1/2 of Blend pot, Master Tone) work as they should (I asked earlier). Pretty much what @adamrobertt is asking, but I have a pretty diagram LOL.

If yes, everything in green is ok.:


Note that 4 of 6 contacts on the push/pull switch aren't greened. Deck 1 of the Blend pot also isn't greened. Check the internal workings of those with your meter as those areas could be the problem.

And I know you checked resistance of the pickups, but maybe verify the actual Neck PU output unless you already know it works. Connecting it directly to the output jack is one way.

Anyway, this is a start. Hope it helps.

The one thing I don't like about this version is when Series is selected, only Deck 1 of the Blend Pot is used. That means only 1/2 of the full pot rotation of Deck 1 will be usefully controllable. The other half of Deck 1 will be full on all the time.