Looking back at your photo of the coil, it's apparent you have copious amounts of non-OEM wiring.Well this morning I removed the Vintage Air ground cables from under the coil and connected them directly to the battery and my issue is still there.
Basically randomly my radio and vintage air AC would shut off and come back on. It's weird cuz my radio is connected to the battery directly and just the on/off wire is running to the Radio fuse in the fuse box. So something before the fuse box is telling it to turn off, I'm guessing maybe a fault ignition key or some ground issue?
Most advice from this forum ASSUMES you have stock wiring. What is that red rectangular box (in your photo) connected to? Is it stock for your FJ40?
Also, " It's weird cuz my radio is connected to the battery directly and just the on/off wire is running to the Radio fuse in the fuse box." needs some decyphering. You should be more specific by identifying "my radio GROUND is connected to the battery" if that is the case.