I am, as they say, an idiot. Or more precisely, self taught at electronics and still learning.
The 12V LED strip is wired in series parallel, with three LEDs to a series. Each series draws about 20 mA. There are about 150 LEDs in the strip, so fifty serieses each drawing 20 mA, for about 1,000 mA.
Which explains why the battery only lasted four hours.
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