I'm pretty sure that it works the same way at USF/IOA but according to their website, you should reserve one in advance to be certain you can get one.
Assistance for Guests With Disabilities
"Wheelchairs are available for rental at $10 per day and Electric Convenience Vehicles ("
ECV's) are available for rental at $40 per day. Each rental requires a $50 deposit (credit card imprint acceptable) or a valid photo ID. To ensure that an ECV is available during your visit, it is recommended that you call (407) 224-4233 at least 24 hours in advance to make a reservation."
If you call the number listed, they should be able to answer your original question also.
Have you considered renting a
scooter for the length of your stay instead of just at the parks? The walk to the parks from the parking lot, the boat dock or any of the onsite hotels is pretty lengthy, too. When my husband had foot surgery a couple of years back, we rented a scooter from Walker Mobility. The price per day was equivilent to the rate charged at the parks but he was able to use it everywhere we went. They deliver right to your hotel and pick it up from the hotel at the end of your stay. They were very dependable and I wouldn't hesitate to recommend them. Here's a link to their website just in case you may be interested.
http://www.walkermobility.com/