To me this sounds like:
You aren't 100% sure or confident with your soldering technique when soldering the pre-tinned wire onto the terminal. And with fully hardened, maximum contact. Are you not using enough heat, or you are soldering wires to terminals without waiting 4 seconds for them to fully harden?
Also what solder, iron and tip are you using?
*If you put pressure on a solder joint and its intermittent, then it needs to be resoldered correctly.
keep findng that intermettence though because it is a clue showing you what to reflow the solder on. It's not a further problem unless the part is faulty or corroded internally.
So yeah pressing or joints for intermittence is a good way to see if they need the solder reflowed or possibly more added. And you don't need much.
I sometimes use a chopstick as a push tester for intermittent connections.
Thanks for the advice. I'm using a fairly high-end soldering iron, Hakko 939. I actually have quite a lot of experience soldering, wiring and building electronics, having done professional electrical engineering work for over 2 decades as well as going through professional solder and inspection training more than once. That may why I am so annoyed with the whole idea of soldering to the back of a potentiometer. It is not something I would ever include in an electrical design. I think it is a horrible way to do a ground electrical connection, and is only done because at the point of first assembly, can be done without any major issues. Try reworking a few times or applying heat repeatedly and you will see that the entire pot can get very hot, and this is just getting it up to the point that the solder will melt. No matter how you slice it, you have to dump a sh!tload of heat into the metal casing to properly melt solder to it and make a solid connection.
What I believe is going on with the pots is that I spent too much time on the leads with the iron wicking off excess solder. I like to clean up a terminal before putting the wire back on. And now I have done this repeatedly with these pots, going back and forth with various tests. Most likely the heat damaged the metallic element (maybe a small PCB trace or copper foil) connecting the terminal to the inner parts of the pot. It works when hot but cools and shrinks, disconnecting the contact. Just speculation but I can assure you, from inspection, the wires are soldered well to the terminals. I have looked at thousands of solder joints in the last couple of decades and know what cold solder joints, disturbed joints and a wide range of other defects look like. I'm not having issues connecting wires to terminals.
Having said all that - this does not address my real problem at all, that being the noise that was present in this bass before I ever touched it with a soldering iron, and that has not changed substantially since I very carefully shielded everything and carefully checked all of the shielding to have <1ohm to ground. I suspect that is has something to do with shielding - the bridge-position pickup is noisy when connected to either pot or when directly connected to the output jack. I swapped in a completely different set of pickups and it has the exact same problem. These were silent when both fully on in a similar bass.
What is baffling me is there is nothing substantially different between these 2 basses (except of the aluminum pickguard). BUT even with the pickguard off, the noise does not cancel well. Not like the other bass that sounds as noiseless as a P-bass when both of the pickups are at full. This bass is nowhere close to that with 2 different sets of pickups.
I appreciate all the help and have tried my best to try all of the suggestions. Unfortunately at this point it doesn't seem like I have found the root of the problem. I still have a J bass that doesn't go dead quiet with both pickups on. And at this stage it is bad enough to be unplayable for recording. It just won't work with this much noise. So I need to find the problem and fix it, or do something drastic. I'm eyeballing the dumpster at the apartment complex down the street at the moment...