Jack, that's a really interesting problem (easy for me to say, I know). I would start by asking whether the car has an alarm (factory or aftermarket). Alarms sometimes make the headlights flash along with honking the horn. A partially broken alarm might cause your problem.

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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