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- Measure the voltage between (+) and (-), beginning on the bulb side.
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With respect, measuring the voltage is only one part of the story, it tells you that there is a circuit, but what it doesn’t tell you is whether there is sufficient current getting through to light the lamp, and in that respect I’m guessing that your bi-colour light uses an incandescent bulb rather than an LED which would light up on far less current.
I had a similar situation with a mast steaming light where the bulb tested good, voltage was getting through, but the bulb would not light up.
The problem was down to corrosion on the copper wiring connections which needed to be thoroughly cleaned back to bare metal in order to allow a sufficient number of amps to flow through to cause the light to illuminate. In other postings elsewhere on the forum some readers have used lemon juice and/or other substances to clean up the wiring connections, but whichever way you do it you need to get your wiring connections back to clean bright metal, and hence the recommendation for using tinned copper wire which does not tarnish anywhere near as readily as ordinary copper wire. If you are lucky a good solder flux and some heat might do the job, as also might lemon juice or plain old fashioned sandpaper, but if you can clean the wire ends well enough to tin the ends with solder then you should be able to get your light working again. If that doesn’t work then your next best solution would be to measure up and get yourself a length of twin core tinned copper wire, and use the old wire as a pull through to feed the new wire into place.
In the past I have used
https://kojaycat.co.uk/epages/950000457.sf/en_US/?ObjectPath=/Shops/950000457/Categories/Cable_Tinned_Flat_Twin for the supply of tinned copper cable in twin and multi core depending on what it was needed for, and found them both reasonable in cost and quick in getting the stuff posted out.