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At some point, the pedal of the other bike had possibly pulled out one of the corroded wires of the singlespeed's rear light on its way out of the door, past the protruding mudguard. When temporarily reconnected it still refused to work, and some further measurements with the multimeter on a rare opportunity to get some fixing done this morning indicated that all the wires were fine but that the light might finally be knackered. I have two spare Seculites+ in the box of bits in the garage but thought I would try the Toplight, originally bought as a potential additional light to fix to the trailer, but also suitable for fixing to the singlespeed's new rack. I also found the cause of the rattle in the right-hand vertical mudguard stay bolt; there's still an intermittent sort of hooting squeak but it's most likely to be the pannier hooks on the rack.