Weird HVAC Issue

[blue62]

Fluctuating voltage....
I would say you have a bad ground or a broken wire.
Or possibly a faulty relay

Continuity testing is not that reliable at telling you the wire is sound.... this is why..
Wires are made up of multiple strands it only takes one strand in that wire to show continuity.
The rest of the strands in the wire can be broken and it will still show continuity.
But the circuit will not function correctly because there is to much resistance in the broken strands for the current to flow.
So if your doing continuity tests you also need to check the resistance on the wire..

You say all the fuses are good how did you check them?
did you check that they are getting power to the power side of the fuse?
In the schematic you linked it shows five fuses at the top right on the first page.
four are hot all the time one is only hot with key on.
There are also two fuses shown at the top of page two
If you have not done so....
You need to test to make sure you have power on the hot side of the fuses.

Find and test or replace associated relays.

At the bottom of page one it show the ground point for the system you need to check that and make sure things are clean and tight.

Those are the things I would start with.