My buddy has a 1200 about the same age as yours, and at one point when the tank was taken off, the small black hose coming off the tank filler drain/overflow got pinched under the tank during re-install. He rides it in all weather, and parks outside sometimes, and the water didn't have a way to drain out, and it started rusting the drain tube from the inside! The tube passes from the little hole next to the filler cap through the tank and out the bottom of the tank towards the back right side. Once the rust became pinholes, he had a very aggravating slow leak that took a long time to figure out!
We finally discovered it after getting tired of yanking the black rubber extension tube out of the way, so I put a rubber vacuum cap on the bottom of the metal drain tube coming out of the tank and the leak went away! It wasn't a great permanent fix because any water getting into that tube can leak into the tank, but it was a good way to problem solve.
Hope you figure things out!