I can assure you that tapping works flawlessly in Mavericks, and Yosemite. It also checks and unchecks fine in the Trackpad prefs. Except of course for the "Tap To Click" checkbox because once you tap it off, then tap is off so it won't turn it back on. Now that you know the problem is not with Mavericks you should first of all trash your prefs, and maybe also trash your cache.
10/16/14 at 9:27am