Car runs rough/stalls when brakes pressed

I added a video to show how it runs rough with the brake pushed in. As I mentioned when I let go of the brake pedal the idle returns to normal.

If I pull the brake booster check valve out of the brake booster I hear the psshhhtt of a good tight vacuum releasing it's vacuum. So I don't think it's the booster or any of the respective hoses. But then I don't understand why pressing the brake would cause the engine to sputter.

The brake booster was replaced in the past year so it's possible but I don't think it's that. My last brake booster was bad, I could hear the vacuum leak when I pressed the brakes and the brakes aren't soft like they were then.

I made a discovery and I think we're getting closer to solving this mystery. I noticed without pressing the brakes if I turned on the headlights or even just the running lights it would cause that extremely rough idle. When I mentioned pressing the brakes, just barely pressing the brake pedal with a finger caused it "with my pinky finger" I didn't push the pedal hard enough to actually create pressure in the system. But I would say it was hard enough for the brake lights to come on indicating I'm braking. So that tells us it's electrical. It's not the brake system causing anything. It was the fact that the brake pedal being pressed turns on the brake lights thus using the electrical.

Once I realized that I started disconnecting the battery, unplugging the PCM and re-plugging etc. And I managed to get the car home but not easily. It took about three hours of stalling pulling over and messing with the battery and PCM.

Now going from here which of the silver computer boxes in the air filter box control the headlights, taillights, brake lights and running lights portion of the electrical system? Because I think it's a wire shorting out on one of these PCM boxes. Just like how the blower motor wire shorts out from being too short on these cars.

I did the test you recommended. The car stalled after clamping the hose so the brake booster is good. It didn't stall immediately but it stalled after about 15 seconds.

The car still runs normal idle until I turn on the running lights, headlights or push the brake pedal enough to engage the brake lights. If I start the car without my foot on the brake and without any lights on and then turn on any of the lights then it idles rough to the point of stalling. If I quickly turn on and off the lights the idle goes rough and then immediately returns to normal upon turning the lights back off.

So I'm still not sure which box it is that runs the electrical system for the lights but I know it's one of the two that are in the air filter.

I think I've isolated the issue to being an electrical connection shorting out at the PCM and that's the only reason disconnecting and reconnecting did something. Because I'm hearing you out where you said it will do nothing but on the contrary it did manage to get the car to drive 6-7 miles back to where I live so I don't have to worry about the car getting towed from the random neighborhood it broke down in. Thank for all your help so far, we're getting closer to figuring this out.

So I've learned that the two computers in the air intake are the PCM and the transmission ECM. I'm assuming the lights would run off the PCM right? Another question, do both have to grounded to the chassis of the vehicle?

Is it possible i'm experiencing symptoms of a bad crankshaft position sensor?

Hey, I just wanted to take the chance the to show what I'm talking about. I've been busy and haven't had a chance to mess with the car at all. So I'm going to upload a video so you can see what's going on. I understand where you're coming from with suspicion of it being a brake booster. And you probably deal with a lot of people who have absolutely no idea what they're doing or how to do the tests you recommend.
Unfortunately, I disconnected negative of battery while trying to get the car home. So I lost the DTCs that had popped up at the time and I didn't have a scan tool with me that day to check it before disconnecting battery.
But I'm telling you I worked on this car since the day I bought it three years ago, and based off what's going on there's something amiss once the vehicle is drawing just any electrical power. I have a brand new battery and I recently replaced the alternator. I'm thinking it could be possible that I got a faulty alternator?
After I installed the new alternator I used a voltmeter and it was holding 14v constant while running but I haven't checked it since all this started happening. It was running great and then I stopped to get gas and that was all she wrote didn't stay running or handle electrical current after that.

In this video I have a voltmeter hooked up to car while I turn the headlights on and cause the car to stall out from the electrical draw. As you can see the battery hold above 12 volts after it stalls, and it stays above 14v while running so the car isn't losing its power at all but yet it stalls out whenever the car draws power.
Picture 1 is while vehicle is off. Shows at 12.20 volts. Picture 2 is while running, shows at 14 volts and then the video of voltmeter as I turn the headlights on and car stalls from electrical draw.

Okay, so all the issues I'm having is solely because the alternator is no good?

My friend, I sincerely appreciate all the help you've been offering but did you read all my posts or watch the videos I attached? (Specifically the one I posted minutes before the voltmeter)

My car keeps stalling out, any time and every time anything electrical draws power from the system. That's what led to the video with the volt meter to show my voltage is good until car stalls. And battery holds good. When it stalled in that video it was because I turned the headlights on. In the other video right before that post I demonstrate how turning on headlights, turn signal, and brake lights all cause the car to stall out or struggle. If I turn the lights off fast enough the car won't stall out and will return to a rough idle.

Plus I mention that I recently replaced the alternator, and asked if it could have been a faulty alternator. So when you said the alternator stopped working in your reply I figured okay so it likely was a bad alternator then. Please if you can, please watch the video I uploaded in the post right before the voltmeter post.

https://www.2carpros.com/images/question_images/410623/video.mp4

Thank you again.

Not that video.
this one:
https://www.2carpros.com/images/question_images/410623/video.mp4