The logic that the ECM uses to activate (close) the exhaust brake seems to vary with factors but I don't think the exhaust brake can be closed when the truck is parked, shifter in Park position, and fast idle activated.
The exhaust brake seems to be closed or partially closed at idle, in Park, when the engine is not yet up to operating temperature but once the engine is up to temperature I don't think the exhaust brake can be closed when stopped in Park.
I preferred the old two speed axle switch on the shifter of my '01 Dodge that allowed me, not the ECM, to decide when the exhaust brake was closed.
The majority of the time my truck is idling at Starbucks it is cold, so with it being cold the exhaust brake will activate even with the fast idle activated