I have a 2720SL and a 2002 Ford Explorer, and I'm not sure what a "standard towing package" is. In 2002, you could get either "no towing package", or an "optional towing package" that included a Class III/IV hitch, 3.73 rear end, aux tranny cooler, and 7-pin wiring harness. If you have a 1-1/4" hitch, my guess is that you have what used to be called "no towing package". Sorry to be a bummer ...
Depending on where and how you tow, you may be able to get away with no aux tranny cooler and no high-numerical-ratio rear end. But you cannot tow a TM without a 7 pin connector and a brake controller. As for the hitch reciever? A 1-1/4" receiver is a Class II hitch. Although it is sometimes advertised as being good for less than 3500 pounds, that is not true for the Explorer, and it will NOT be adequate for towing any TM. Even the TM website, which is as optimistic as it can realistically be, says "We recommend using a Class 3 hitch with load equalizing bars for most vehicles (not necessary on heavy trucks)". An Explorer does not count as a "heavy truck", believe me!
You need to spend some time with the Ford Explorer towing guide. The 2003 version is available at
https://www.fleet.ford.com/showroom/...s_Windstar.pdf
Again, sorry to be a bummer, but I hate to send someone out without an adequate setup. Your life (and that of your family members) could be at stake. Not to mention a lot of wear and tear and repair on your truck.
Bill