The ABS light comes on and the radio seems to fade?

Hello,

The ABS light gets triggered when the ABS system detects any fault within.
It could be due to a faulty sensor, bad wiring or the module.

https://www.2carpros.com/articles/abs-warning-light-on-easy-repair-guide

The best course of action would be to scan and retrieve the ABS code(s). That can help with the diagnostics of what might be triggering the light.

Here is a helpful video on how to retrieve ABS codes:

https://youtu.be/rTtAnsOlZU4

As for the constant clicking. Where is the noise coming from? Typically, a faulty relay can click.
Do you have any component that is inoperative?
You might have to look at the fuse panel inside the vehicle to see if you can determine which relay is clicking.

If the clicking only exists when the A/C or heat is on, then it could be due to an air door actuator.

Please let me know if you have any questions.
Thank you.