There's no stupid questions in the electronics cavity of an Alembic!
You definitely have a grounding problem here, which is worse on the bridge pickup.
The pickup leads are the two gray colored wire bundles that are coming in from the hole on the top of the cavity. They are looped together through a ferrite bead (this helps kill off high frequency RFI noise, then each lead goes off to a separate connector which is plugged into the main EQ board.
The pickup connectors are the two brown colored plugs on the EQ board next to the bright blue trimpots. If you gently unplug these connectors, you can disconnect or reverse the pickups on the pan pot.
I think the other wire coming into the cavity must be the power supply from the battery, also coming through a ferrite.
Turn the volume on your amp down to a low level before you do anything in the compartment. You can generate large transient pulses when you disconnect or connect things, and you don't want to damage your amp.
The first thing I'd do is gently wiggle everything in the compartment to see if you can isolate the source of the hum.
Everything in the audio path can potentially pick up hum from the outside world. The way that guitars prevent this is to build a cage around the audio path and connect that to electrical ground. Any noise that's picked up is then sent to ground without getting into the circuit. The pickups are designed to pick up noise, but they have a special coil inside the pickup that eliminates much of that noise. The inside of the compartment is coated with conductive paint, so it shields a lot of the electronics. Things that poke through the compartment like the pots, jack, and switches have their cases intentionally grounded so they act as part of the shield as well.
The problem with your bass is that there's something that's become disconnected from this network of shielding. Instead of blocking noise, it's picking noise up and injecting it into the audio.
The first thing I'd try is to gently wiggle the red pickup connectors and the other red plugs in the compartment. I'm pretty sure the red plug in the bottom left of the picture is power, so you can wiggle that one, but don't unplug it while your bass is plugged into the amp (you'll get an enormous boom if you unplug it).
Next I'd gently wiggle the ferrites, the board, the jacks, and pots and the back side of the switches. You don't want to force anything at all, just a gentle bump. If there's a failed connection somewhere, when you jiggle the parts, you may reestablish the connection and the hum will go away.
The three things I'd really suspect here are the pickup plugs - one may have become intermittent or that the ferrite beads may be touching something that should have been insulated. The third thing is to see if the output jack has lost contact with the shield (unlike most of the stuff in the cavity, the output jack can get stressed from the outside world).
I would also unplug each pickup individually and see if the problem goes away (of course, one of the pickups will go away too).
One other things that's very unlikely, but easy to do... Wrap your battery with electrical tape. I doubt that the battery compartment is painted with silver paint, but if it is, grounding or not grounding the metal case of the battery can be an issue.
Try this stuff and report back!
David Fung