I understand from reading the forums that an employer doesn't have to give breaks to employees under many circumstances. However, can they force you to clock out for the breaks they do elect to give you? And can they make you clock out for a specified amount of time rather than just the amount of time you're on a break?

Well, they can make you clock out for rest breaks, but they can't NOT pay you for them if the breaks are less than 20 minutes in length.
http://www.dol.gov/dol/allcfr/ESA/Title_29/Part_785/29CFR785.18.htm