i personally would go for a bit 2x1" screwed near the tile baton
or at minimum pilot into the tile baton and use a say 50mm wood screw and give a good "heave" on the baton but holding on well with the other hand to check it wont give as some tile batons can put knotty pine to shame
or at minimum pilot into the tile baton and use a say 50mm wood screw and give a good "heave" on the baton but holding on well with the other hand to check it wont give as some tile batons can put knotty pine to shame