With my in-laws, we had this issue one day, and it was probably the better part of 10 years ago. They rented an EV in the morning, stayed till mid-afternoon. Then we park hopped, took our receipt to get one at the next park. They had none.
Called an offsite vendor, and one was waiting at the hotel for us when we got back. The bellhop showed my MiL how to use it.
Worked out great. Had it for the remainder of the trip. If memory serves me correct, I think the one week rental paid for itself in two days compared to Disney.
Been a few years since my in-laws traveled with us, so not sure what it is like today.