Are the brake lights dim?
Do the brake lights work when the parking lights are on?
It could be a bad ground. You usually see this with a trailer having a rusty connection to the tow vehicle, but it could happen elsewhere. Usually, in that case the taillights OR the brake lights work, but not together.
With the taillights off and a bad ground, the power from the brake lamp filament in the bulb continues into the parking light filament, and then goes to ground through other parking light bulbs elsewhere in the vehicle. The taillights would work in the opposite direction. Since the brake light is normally brighter, it has a lower resistance in order to draw more current. So the parking lights would ground through two low resistance brake light filaments in series and be reasonably bright. When you step on the brakes, the junction between the two brake lights goes hot and the taillights lose their ground path. With both filaments hot at the ungrounded socket, both the brake and taillight will go out until one or the other is turned off to establish a ground path again.
So with a the brake lights instead of the taillights, they would ground (dimly) through a higher resistance in the same bulb, but then all the turned off parking and possibly also marker lights would be in parallel going to ground and lower the resistance to that part of the series-parallel network.
As I said, if it is a bad ground to the socket, the brake lights should stop working when the taillights are turned on. If not, look at the bulb and the other wiring fixes.
P.S. The buttons on the bulbs are generally blobs of lead-based solder, and they will get a high-resistance powdery tarnish on the surfaces with age. I have brought many a "dead" bulb back to life by vigorously rubbing the buttons on my jeans to polish them until they are shiny again.
Someone said "Making good decisions comes from experience, experience comes from bad decisions." I say there are three kinds of people: those who learn from their mistakes, those who learn from the mistakes of others, and those who never learn.