I have a 1995 Olds Cutlass Supreme with a factory cassette car stereo(non-Bose) and the display has started to blink when I apply the brake on the car.

At first I thought it was a bulb issue but it'* fine when I'm not using the brake. Is it still a bulb issue or.....?

You mean the numbers and letters are blinking?

Can you shoot a video and post it to Youtube?

A video would help.
Is it dimming, or flashing like it may be shorting somehow?

The whole display. Just flashing , no dimming.

I'll shoot a video tomorrow.

Tried to see if I could find anything about others having that issue, I found some talk of a similar, but not that exact issue.
Others mention turn signals flashing faster, and traction control light issues, they mention the grounding pin in the pigtail for the rear tail light assemble as being burnt, I don't think that is your issue, but it could be somewhat related, so I figured I'd mention it.
Will check out your video tomorrow when you post it.

Before I go on I must mention this(I also mentioned it in my public profile for this car) I added electronic flashers(2) and LED bulbs(turn signals, brake lights). It also has had a remote start for the past 3 years without any problems.

When I went in to make the video I noticed now that the display goes totally out when I apply the brake. Now while the brake is applied and I use the turn signal the stereo display flashes on and off with the signal. If I take my foot off the brake and turn off the turn signals then switch on the hazards the stereo display flashes on and off with it along with a beeping. The rest of the car operates fine, drives and operates normally along with nothing lit up in the dash.

Should I still do the video? Wondering if TheftLock has something to do with this?

This is getting weirder. Went out for errands and slowly the radio display blink on braking/turn signals went 90% away but I still have audible beeping when I have the hazards on, no radio display blinking though. It'* the same beeping that happens when you leave the keys in the ignition or the headlights on.

Check all of your battery connections for corrosion and tightness of connections.

Yeah, I checked the battery connections already. They're ok, no oxidation. I moved the wiring around under the dash and it affected the radio display so tomorrow or this weekend I'm going to remove the underdash and give it a good look. I was thinking also maybe the brake pedal switch?

Well I disconnected my battery to "reboot" my car, didn't fix it. Removed fuses to check them, didn't fix it. Took car to local GM dealership to check it out and get the theftlock code for the radio(from the fuses), didn't find anything.

If I have to I'll just live with it.

I have another problem and didn't really want to start another thread on it as it might be related. Whenever I engage my hazards the car also beeps UNLESS the car is running then no beeps. This problem I'd like to solve.