I changed my transmission gear oil today and noticed that when I put it into Reverse my radio goes off and then on. It did blow the fuse once. It's a 4 speed. I was using Passon Perf gear oil and switched to 85W90 gear oil. I did add the trunk light harness that is behind the drivers side kick panel. I don't remember if it did this before adding the trunk light harness. The stereo is an aftermarket one which I put in about 20 years ago. Could it be a bad reverse switch at the tranny?

Unless you have done some home made wiring the radio has nothing to do with the reverse light switch on the trans.

does it do it consistently or is it intermittent?

Oddly I have the same issue, but it is an automatic in my coronet.

It does it every time I put it in reverse. I believe it started right after I changed the tranny fluid today.

I have not dug into mine yet.
the only thing I can think of is a grounding issue.
when the reverse lights come on, the dash light for yours comes on too I believe.
depending on where you grounded your radio, would be the only thing in common with going into reverse as stumpy said, the wiring doesn't cross over like that.

I'd put the old fluid back in............

OK, I've never heard of such an issue before - pretty baffling!

Maybe the car thinks it's 2019. I think in one of my new cars the radio goes out in reverse to keep from distracting you.

Does it do with the key at 'On' and the engine not running?

So I unplugged the plug to the reverse switch on the tranny. Car on accessory put it into reverse the radio stays on. No reverse light on the dash since it is unplugged. Hooked up a jumper wire from one female to the other female lead on the plug. Car on accessory the reverse light on the dash is on. Put it into reverse and the radio stayed on. To me it sounds like a bad back up light switch.

leave the jumper to keep the reverse light on without the switch plugged in, and start the car. see if the radio stays on or dies.
If it stays on, then shift into reverse and see if it still stays on.

Can you replicate it dying in accessory mode?

I will try it again tomorrow with the car running. I have been doing this in accessory with the car off.

The reverse light is on the same power line as the radio...
Sounds like the reverse light switch has an intermittent short to ground issue. EZ to check with a continuity light, unplug the connector on the trans switch, put the transmission in reverse and check if any continuity to ground from either terminal. I had the same issue with my 70 RR 4-speed... Later replacement switches from China are known to have issues..

Just my $0.02...

Are you talking about checking the continuity with a test light on the switch or the connector?
I unplugged the plug and hooked up a test light. I put it in reverse. Grounded the test light and then touched the each terminal on the switch. No light from either side. Did the same with the plug. Light came on and radio stayed on. Bad back up switch?

When doing the test, ignition should be ON.. Ur test was correct for checking a shorted switch, but maybe its intermittant... When the trans is in reverse U should have continuity between the (2) switch terminals, but nothing to ground. But as I said previously the aftermarket OE replacement switches from China are strange, my suggestion would be REPLACE it. If U were in SoCal I would give U 1 I have about (5) spares....

Just my $0.02...

Thanks for the help. I'm getting a new switch tomorrow. I did do it with the ignition on. The switch is about 15 years old.

So I got a new back up switch yesterday. Plugged the plug to the new switch and pressed the ball bearing. The reverse light went on and the radio stayed on. I touched the switch to the trans for a ground and pressed the ball bearing. Reverse light went on and the radio stayed on. Looks like it was the switch. Thanks Sinitro.
Now to pull the switch out without removing the shifter mechanism is a different story.

Nice...
Happy to assist..
Hope all works out..

Just my $0.02...