The Mazda 3 wasn't offered in the US in 2002. However, I believe the same vehicle was offered in Canada called the Protege SE. That is the only one that I have info on that has a 1.6L engine.
I went through the wiring schematics for the radio, interior lighting, and central locking. There is one common link that involves all of them, the Room Fuse (10 amp).
Do me a favor. The radio fuse and room fuses are behind the left kick panel. See pic 1 below. When you remove to inspect or reinstall, make sure the key is in the off position. If you leave the key in the on position, the malfunction indicator light will stay on.
I also attached the wiring schematics for the radio. However, I feel the Room fuse is the issue. I attached it so you have a reference.
When you check the fuse, make sure it is good. Also, check to make sure there is power to and from it.
Here is a link you may find helpful:
Let me know what you find or if you have questions.
See pics below. Please note that this is from a Protege. It should be the same or slightly different.
Images (Click to enlarge)
Sunday, August 14th, 2022 AT 8:52 PM