So what happens if the headlights are NOT on and you press on the brake? I assume that all is well, though you did not say. In the case of "momentary" lamps like brake lamps, the indicator is functioning correctly when it stays on. When the headlights are ON, the taillights are also ON; it's possible that you have a bad ground at one of the brake lights so that, with the tail lights OFF, the brake light can ground through the tail light circuit. With tail lights ON, the brake light can't work, draws no current, sets off the alarm. Have you had someone stand behind the car and look as you turn lights on and off, press on the brakes, etc.?

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"Buster" in the '95

Our all-Diesel family
1996 E300D (W210) . .338,000 miles Wife's car
2005 E320 CDI . . 113,000 miles My car
Santa Rosa population 176,762 (2022)
Total. . . . . . . . . . . . 627,762
"Oh lord won't you buy me a Mercedes Benz."
-- Janis Joplin, October 1, 1970