I have a 98 ST2 with a strange electrical problem . No rear light or brake lights . If i fiddle with the cable to the rear light i get the tail lamp to come on but it all goes out when I put the brake lamp on. Ive had some other issues with connectors and have had to chop some out as they were all rotten but so I suspect the same but cant figure out where it is? The connection at the back of the lamp are a but cruddy but seem sound,
Trouble with the ST2 is that when the rear light unit is fitted to the bike, the cables and connections at the rear light bulb are just about touching the metal brace at the rear of the frame. Ducati used right angled Lucar connectors there to try and avoid any rubbing that would cause a short. I removed mine and cut a U section out of the bracing so that I could use new cable and straight Lucar connectors on it. I then gutted the rear light and fitted a home made LED array instead, that move all the connectors out of the way. Beware if you remove the rear light to completely rewire (easy to do) as the bulb holder plastic becomes brittle over time and once it is in more than two pieces, it is hard to glue back together. Have a look at some of the older posts on my blog and you might see some pictures.
It's a problem with the earth. The tail light is managing to find an earth return through the brake light circuit. When you put the brake light on there is 12v at both sides of the bulb so it goes out. You'd be best to strip it down and clean all the connections properly making sure there is continuity from the 3 pin connector at the harness back to the lamp contacts.= through each of the three wires.
