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How cold is cold, 32F or 50F or what? Also, the figure was a little confusing!!! Is the battery connected to charge at both the top and bottom? If so, then light could be on whenever the battery is being charged, but off when in motion,

Normal winter night temp in the stairway is 25-45, with a few nights 10-25.

Charging contacts are at top and bottom. Chair is at top nearly all the time.

Only need resistor or lamp on when charging.