Hi,
The idea that this happens when you press the brakes leads me to believe there may be an issue with the vacuum brake booster. The booster is what provides power brakes for you. It is actuated by engine vacuum, so if there is a change in how the engine runs and in the brake pedal, I suspect that either there is a leak in the vacuum hose between the intake manifold and the brake booster, or the booster isn't maintaining vacuum (leaking) and the engine is hit hard for vacuum when you apply the brakes.
So, here is what I want you to do. First, inspect for engine vacuum leaks. Here is a link that explains how this is done:
https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge
Also, the brake booster is mounted to the firewall under the hood on the driver's side. The brake master cylinder is attached to the front of the booster. I found a pic of the booster and highlighted where the vacuum hose attaches. Locate that and follow it back to the engine. Inspect it for damage, dry rot, or anything that could create a leak.
If you don't find a leak, the problem could be internal. I attached the diagnostics below for testing the brake booster. It will require a vacuum gauge, but oftentimes a parts store will lend one to you. Note: The first two tests require no tools. In the remaining pictures, our primary focus is vacuum. I highlighted the gauge you will need. You will need a T fitting for the gauge to be connected between the engine and booster. Tell them at the parts store that is what you are checking. Our primary focus is how long and how well the booster holds vacuum.
Take a look through the directions below and let me know if it is something you feel comfortable doing. One last thing. Between the engine and booster, there is a check valve in the vacuum hose. That is to prevent vacuum from going the wrong direction. Therefore, you should only be able to direct vacuum through in one direction. If it goes both ways, replace the check valve.
Take care,
Joe
See pics below.
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Sunday, August 29th, 2021 AT 8:09 PM