I'm certainly no expert on this but didn't see this mentioned in your thread, so thought it worth bringing up.
It may be the "cancel" connection in your turn signal switch. With two filament bulbs, one is for your driving lights and the other is your turn signal/brake light. When your brakes are on, and you turn your signal on, your turn signal devise cancels the current to your brake light on that side, and sends current to the signal.
It seems like the problem you are experiencing may be related to this. Bill and others are much more knowledgeable than I am and can comment about this. Good luck! (I don't like electrical problems!)
~ Victor
1941 3/4-Ton Pickup (in process). Read about it
in the DITY Gallery1955 Grumman Kurbside "Doughboy" 235/3 on tree w/ OD
1957 3100 - moved on
1959 C4500 Short Bus "Magic Bus" - moved on
1959 G3800 1 Ton Dually "Chief" - moved on
1958 C4400 Viking "Thor" ~
moved on to fellow Bolter