I don't have any experience with Eclipse trailers, but you shouldn't need to get a super light weight trailer with an F-150 (assuming it has the factory tow package) If you don't already know its tow capacity find out (any Ford dealer should be able to look up the VIN and confirm)
I have a steel two-horse slant with small-ish tack room, and it weighs 3000 lbs empty. Fully loaded it's right around 5500 lbs, which my Tundra pulls just fine. IIRC the Tundra and F-150 are about the same class, towing-wise.
Make sure you get a good brake controller and learn how to adjust it properly.
One thing I wish I had known earlier was the advantages of weight distribution systems. I'll be getting one put on my trailer when I take it in to get it's annual service in the next month or so.
“The horse is a mirror to your soul. Sometimes you might not like what you see. Sometimes you will.” - Buck Brannaman
"Nothing forced can ever be beautiful." - Xenophon