put our Heads Together
Join Date: Jun 2003
Location: southeast pennsylvania
Bikes: a mountain bike with a cargo box on the back and aero bars on the front. an old well-worn dahon folding bike
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The brake cutoff wires are probably designed to output, at most, a small fraction of 1 watt, at 5 volts. Your lamp is probably designed to receive at least 5 watts and it won't work at very-low power.
Put another way, the amperage maximum on your brake cutoff wires is very small, and if you go over that amperage maximum the voltage drops and you're no longer getting 5 volts (more like 0.1 volts) and your light doesn't work at 0.1 volts.