When I first got my Georgetown, I would get the odd drop of water coming off the handle of the TV antenna. My antenna had about the same amount of sealant around the antenna base as yours. Looking at it, I figured the sealant would contain water around the bearing surface of the antenna where it turns. I recall there being a lip under the moving part to stop water entering, but the excessive sealant looked like it could contain enough water to go over the lip. I cut a few drainage channels in the sealant to stop the pooling water. The other thing I did was snug down the A/C securing screws. My front A/C is not far from the antenna. There are 4 screws, accessible by removing the filter cover. Mine were quite loose, which I gather tends to happen as the A/C gasket compresses. You don't need to really come on to these screws, but they should be snug.
After doing these things, my leak stopped.
Hope you get it sorted out!