|The "sap" is either dark brown or black|
I don't even really thump watermelons anymore, I just look for the black spots. Yes, black spots. Sometimes very dark brown spots.
My mom used to tell me to look for the rough brown patches on a watermelon because "that's where the bees kissed it," but I've taken it a step further. Not only do I look for brown patches, but within the brown patches I look for black sap. That's the sugar, I believe, coming out because the watermelon is so sweet.
Try it and let me know if it works for you. Oh, and the watermelon in the pic is perfectly sweet and perfectly textured.