There's a lot of information that has to be known for most answers. As you can read from the answers to many similar questions, it all depends on your specific gun. So a lot information has to be known to start with what will amount to guidelines rather than specifics.
The one specific to be determined is what is the true bore diameter of your gun? The second is do you want to shot with a lubricated patch or using a bare ball with wads. Some guns perform better with one method to the others even from the same builder.
TotW is making recommendations based on a 20 gauge bore being 0.615" in diameter. For that application with a lubricated patch with ball, the ball could measure about one patch thickness less than the bore. In this case that would be 0.600" ball and a 0.017" patch.
A 62 caliber will have a bore of 0.620" and may be rifled. There a good recommendation would be the 0.610 ball and a 0.017" patch for a tight fit.
If you want to shoot the 20 gauge using wads and a bare ball, the 0.610 might work well. You will need the over powder wad, maybe a bit of tow to wrap the ball in the center of the bore and an over shot card to hold the load in place.
With that all said, there are users of 20 gauge fowlers and fusils that have good success with a heavy lubricated patch of 0.022" and a 0.590" ball. Some have even used a smaller ball.
Buy some balls to experiment with both a lubricated patch with ball and wads to hold a bare ball load. Actually tow (flax fiber) can be used for over powder, ball wrap and over ball wadding.
Start this experiment off with the measurement of the bore and get several ball sizes to experiment with.
Your question just isn't an easy one to answer.