they open for the beginning of EMH at 8am, and they usually close 45 minutes after the official park closing time that day (but they will have a sign up on the door giving you this information when you leave your bags there).
We checked yesterday for dropping our bags today. 8 am for the EMH and it was free or up to 3 items per AP. We checked 5 things this morning and was very glad not to have to pay.