SML,
Well Sir, this is REALLY interesting now. Let's see, a third brake light that's supposed to be, according to CC, wired to one or the other, or both, rear brake lights and, the coach has no amber turn signals which, would be ok to wire the third brake light to the existing two brake lights if it did have amber turns.
But, it doesn't have amber turn signals. OK, now, let me ask you this, just how is your lighting situation arranged back there? Do you possibly have separate "Red" turn signals from "Red" brake lights? I've seen some coaches with more tail lights back there than Carter has liver pills. (Way old school joke) (not many would know it)
If so, then you'd have dedicated brake lights that would be unaffected by turn signal operations and THEN you could have that third brake light wired into those.
Now, one poster has commented on the ebrake having an effect on it. Well, yes about 99.9% of the ebrakes will activate the brake lights. Just exactly how it's tied into that regular brake light system, I have no clue. I suppose diodes (even though they, at CC said there was none, switching relays etc. could be involved) all that stuff is light years above me. But, is sure is going to be neat to learn what the cause was/is.
Scott