1. The 2005 Sienna is rated for 3500 lbs towing. The 2005's supposedly have the towing package across the board. Regardless, I added a separate transmission cooler (fairly trivial job).
2. 2nd gen Sienna's and later sit LOW and have relatively soft suspension. I use a 2" receiver hitch, with a 4" rise tongue. A set of Firestone airbags helped immeasureably for towing when the van is loaded. Even so, dragging the hitch is fairly common when crossing curbs, yards and such.
3. Towing a 12' tandem flatbed (about 2k lbs with cargo) was smooth and hardly effected mileage at highway speed. Towing a 5x10 enclosed (taller than van) cut the mileage in half and had it searching for gears. A severe headwind had me ducking off the highway and looking for quieter backroads.
4. The wiring harness mounts in the jack stowage area in the right rear. Easy access to the vehicle's wiring and you need a conversion box. The trailer harness gets rolled up and stowed in there and poked out the rear door weatherstrip when needed. It's actually a GOOD thing and keeps the harness and wires clean and undamaged and prevents corrosion.
5. Couple of notes about the Sienna.
A. It's known to have radiator leaks at higher mileage. Luckily it's usually self sealing, but pay attention pre and post trip.
B. The 3.3 using a timing BELT. If you're regularly towing, make sure you change it between 80k and 100k. There are kits that supply seals, gaskets and a new water pump, go this route. Labor is $350-500.
So, it'll tow and do it fairly well even up to near it's capacity. Still, it's not a TRUCK with the suspension, rear end, torque/hp, and ground clearance to make it trivial. Tow wisely. Stabilizers at regular 3000lbs would be a good idea as would electric brakes.