I doubt it's a relay, nothing that affects the ABS should affect the radio and vice versa. The radio's main power is via the fusible link box and Accessory Relay, where the ABS gets power from its own dedicated fusible links. I'm afraid you're probably chasing a ground gremlin. For the right way to chase them, consult this post:
topic628130.html
In this case, I would pay as much attention to the chassis grounds as the engine, since the ABS doesn't share the engine ground bus except through the main cable. It wouldn't surprise me if your P1145 was coming from the same source, the cam sensors are both grounded to a bracket at the front of the engine.