The circuit is simply three-components across the 24VAC supply: a two-wire photocell and two 12V (1156 auto bulbs) in series. One would expect that the resistance of the photocell is close to zero in the dark, to apply the full voltage across the bulbs, and highest in daylight to turn them off.
My actual measurements on the cell alone are opposite: about 10,000 ohms in bright light and close to infinity in the dark. Thinking the cell was bad, I ordered a replacement; same oddball measurements.
What am I missing? My ohmmeter uses a 1.5 volt battery.
It turns out that the problem was a bad crimp where one of the wires going to the center contact in one socket was bad.
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