That is not answering my question, let me be clear: How did you "check the battery and alternator"?

It is one thing to monitor and verify alternator production - altho I'd caution you, when my alternator went out, it would charge fine when the engine/alternator were below about 100F, but above that, the alternator would swing between 10 and 16 volts, this fooled me at first until I put an analog meter on and drove with it for a day.

As to the battery - that's not easy to verify without a pretty fast scope on the B+ line coming from the RCM. Easier to just replace the battery. (See point 2 below.)

The brake controller appears (and again, I am going only by what you have typed) to be having a very bad day. The #1 cause for this is unstable electrical supply to the brake controller. THe causes we have seen for this in the last sixteen years are:
1) Unstable alternator output.
2) Battery with insufficient capacitive reactance. (Note I did not say that the battery is "weak", altho in some cases, that is true as well.)
3) Bad RCM (In your case, the symptoms make me doubt this one but it is, again, hard to disregard the possible.)

I've been here 16 years, I've lost count of the number of individuals who show up and tell us "the battery and alternator are fine" who THEN come back in three weeks to tell us they replaced one of the two and the issues all went away.
My SE's battery started the car fine - but my wing/brake controller/etc were insane until I replaced my (two year old) battery.