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Assuming the running lights are working I would start by replacing the bulb with a known good bulb. Bet there's a cross at your local auto parts store but I have no idea what it would be. If you pull the bulb and take it in, a good parts guy can probably find it, though. If you're going with an official HD bulb the part is 68165-64
As Wuffle said, replace the bulb. After a lot of years the contact points on those old bulbs just don't make contact anymore. Also, look for corrosion in the socket.
If that doesn't do the trick, buy a cheap digital VOM (volt-ohm-meter) and check for voltage at each connection point. It is simple to do. Set the VOM on the 20 VDC setting, the black probe on a ground point and start probing (carefully) with the red probe. You should see battery voltage at each connector.
The wire runs back from the tail light under the fender, to a hole in the left side of the fender, back along the fender strut to a plug under the left side plastic cover. Check the pins at that plug with your meter. I don't remember what color the brake light is off-hand.
Next, get under the bike and look at the switch on the rear master cylinder. Put your meter on there. You should have +12v on one pin when the ignition is turned on and on both when the ignition is on and the brake is depressed pretty hard (not lightly).
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