What I would do, as a "technician/troubleshoot" would be to actually measure and monitor the voltage at the battery and some of the connectors where the power is distributed (any of the fuses for the lights and/or dashboard).
To do this, you would probably need and "old style" multimeter - the kind with and actual needle on it that moves up and down to show you the voltage.
What I suspect is happening is that the alternator (generator really) is not doing a good just of regulating its output. In other words, the internal regulator, which is inside the generator, may be sending "pulses of power" instead of a nice steady flow of current to the electrical system.
So what you would need to do is have a specific test done on the generator to test for this. The trouble is, most shops will only measure for total current output, and the equipment used to this "averages" the readings and will not show the tech these pulses of power.
You can TRY to see these pulses with a modern digital multimeter, but they tend to average too, when set on the DC scale. Or you can set it to the AC scale and see if you get anything other than 0 volts. I would think that even a couple of volts of AC, that is not supposed to be there, would make the lights appear to flicker.
I would think that using "the shotgun method" (just replacing parts), a typical auto tech would replace the generator. But I would really want to find the root cause before replacing something like that and then charging the customer for it, even if it do not fix the problem.
So my "short answer" would be to have a more extensive test done to find the source of the flickering.
The brake pedal could be a part of the issue - anything is possible. To test this theory, disconnect it for a few minutes and test the system. But since you said that it does it at idle, I would think that the brake light switch is not the cause.
And yes, you are reaching for answers - but that is OK. If something bothers or annoys us, we tend to want it fixed or taken away.
I have a similar issue with my Chevy minivan that bugs me, but just a little bit. It only does it when the Secondary Air pump kicks on, which draws a lot of current when it starts up, and I only notice it at night. I suspect my battery is getting weak (original), and I don't want to replace it right now, so I will "live with it" until it gets worse.
I hope this helps and gives you some guidance as to how you will proceed.
Take Care, Greg A.