Now for the next option for finding a rental smaller sized travel trailer. There are companies that act as online rental agencies for persons renting out their own personal property RVs. Rather like an air BNB business website. Those individual renters do not turn up on a standard keyword search. You have to search out the rental agencies and then look at their inventory offerings in the locations closest to where you want to go.
The company Outdoorsy is one such place. Here is a teardrop trailer on their current offerings list in the Phoenix region.
See 20 photos of this 2021 Pindrop Travel Trailers Fina Roma Travel trailer in Phoenix, AZ for rent now at $99.00/night https://www.outdoorsy.com/rv-rental...k&utm_medium=affiliate&cam=58&subcam=40661_NA
They do have other small travel trailers including some pop ups.
Good luck with your hunt, the little rental trailers are out there but finding exactly where will require sifting them out of hiding inside of various types of rental agencies. Remember small does not mean cheap to rent!