The cruise control amplifier uses the brake light "hot lead" as a reference ground. When your foot is off the brake pedal, that connection is seen as ground even though it goes through the brake lamp filament to the actual ground connection. When that circuit is energised by the driver stepping on the brake pedal, the ground goes away (becomes +12v) and the cruise control is disengaged.

The wattage of the bulb is not a factor, internet rumors aside. Putting an LED into the circuit may have changed things just enough for the CC amp to not "see" a ground and therefore not turn on.

Good catch,

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Norm in NJ
Next oil change at 230,000miles