Rough idle

Welcome to 2CarPros.

It sounds like you have an engine vacuum leak. It could be the brake booster itself. Here is a link that shows in general how to check for an engine vacuum leak:

https://www.2carpros.com/articles/how-to-use-an-engine-vacuum-gauge

Now, the power brake booster is mounted under the hood on the firewall (driver's side). The brake master cylinder mounts to the front of it. First locate that. Once you do, you will see a large ribber vacuum hose attached to it. It attached to the vacuum check valve. I need you to confirm there are no leaks at that point or any point in that hose.

I attached two exploded pics of the booster. I circled the check valve in both. Since the problem happens when you apply the brakes, I have a feeling the booster needs replaced, but check for leaks first.

As far as the brake booster, you need a vacuum pump to see if it holds vacuum. Basically, you attach the pump/vacuum gauge to the booster and apply vacuum. The booster should maintain that vacuum without it dropping. Most parts stores will lend you a vacuum pump to test this.

Let me know what you find or if you have other questions.

Take care,
Joe