The '01 you are looking at, why do you state it is a "dealer installed" towing package (seller stated so???)? Did this truck not have the factory tow package? If not the factory installed package and it was dealer installed, did they install a trans cooler along with the receiver hitch and 7 pin plug? You will want a trans cooler for sure.
Also look in the glove box for the rear gear ratio code. You will want at least the 3.73, if not the 4.10 gears for that trailer depending on what motor the truck has (4.8 or 5.3???) since that truck only has a 4spd trans.
Does the truck have the GM factory hitch? If so, that design has known issues of failing. I would suggest a square tube hitch because round tube models can "wind up" (twist) when you latch up the wd bars.
Good luck!!!