The website will not display cars after you hit the SEARCH button if the location is closed.
Please conduct a search for the 24:30 hrs (as your flight arrives at 23:55 so you will have plenty of time to collect your luggage and also get to the rental car supplier desk) and you will be offered what is available at that time in the morning at Pisa Airport.
Tip:- When booking the car, please do not forget to enter your flight number so the provider will be aware of any possible delay.