I am an electrical-electronics engineer.
I may shed some light (hopefully making sense) on how the CCA can be influenced by the Brake Light Bulbs as to make it disfunctional.
If I remember correctly, Pin# 8 of the CCA reads a ground thru the brake lights (filaments or base, I do not know).
When the brake is applied, the circuit is opened and the resistance becomes infinity, hence disengaging the CC.
IF the resistance (of the bulbs or the casing?) is greater than whatever resistance it is supposed to read (brakes not applied), it will see it as an open circuit, hence making the CCA inoperable. It will make it think the brake is constantly applied, hence keeping it permanently disengaged.
Keep in mind, ground does not necessarily means 0 Ohms. All circuits have thresholds.
I hope this explanation makes sense.
In my humble opinion, I believe the theory of the bulbs affecting the CC is valid.
1999 Porsche 996 Carrera Convertible
1994 420E - SOLD
1986 300E - SOLD, what a car