The excess varnish was being picked up by the paper towels, while at the same time leaving enough behind to keep the painting a bit glossy. One of he major problems in the first place was that the varnish had become thicker as the thinner in it evaporated from the bottle. This is what caused it to take longer to dry allowing it to create drips.
After removing the varnish I applied a new coat, this time it was thinned down with more turpentine, this made the varnish level out quicker and it also became more flexible, not leaving any brush marks behind.
Another thing I discovered is that a good soft synthetic varnishing brush works a lot better than a natural hair soft brush. It didn't leave hairs or other strange debris behind. Now my painting is drip free and ready for showing, that's if I knew where to submit the painting.
On the Pan, oil on panel, 2009-2011, 24 x 20 inches