Picking a watermelon at the peak of ripeness is really tough. I’ve tried looking for color change on the bottom, condition of the tendril nearest the melon, and the thump test. All of these techniques are pretty tough to master.
However, I have one method that has never let me down and if you don’t have too many vines, it is fairly easy. Watch your female flowers and when the fruit sets, stick a pop-sicle stick in the ground next to it with the date written on it. If you find one that has been set for a few days, just back date your marker. Pick your ripe melon 33 days later. It should be pretty close to perfect. If it is a little green for your tastes, pick the next melon at 35 or 36 days. If it is a little over ripe for your tastes, pick the next melon at 30 or 31 days. Once you dial in the number of days that you like, it is pretty much fool proof. 33 days works pretty good for varieties that grow to 8 to 20 lbs. I have not grown the big melons, they may take a little longer.