Its not what you can tow.
Its what you do tow. So if youre towing over 10k its considered commercial and yes you do need a class A.
There are exceptions for farmers, firemen and rvs on weight restrictions of the primary vehicle.
Even in Cslifornia, one of the strictest states in the nation, you dont need a cdl due to the air over hydraulic brakes on a deuce (according to enclyopedia) because Ca. recognizes the hydraulic aspect of the braking system as being the primary aspect of the overall system, thus, reportedly, they do not require a cdl there for a deuce either.
Anyway, when I asked, I was told it was not needed. I dont really know of anyone who got a cdl in Ga. for a deuce.