But should I also check the wires going from the empeg itself to the radio module? COuld they be responsible for a weakening signal?

Of course. All wires should be checked, including the antenna wire, and whatever wire is powering your antenna amplifier.

If you have another old car stereo lying around, it might not hurt to temporarily plug it in to see if it, too, gets reception problems. Maybe it's the car's antenna amplifier failing.