2001 F150 4.6
Trailer gross weight is 2990, trailer weighs 1000 lbs so payload is maximum 1990 lbs. I understand overdrive should be off as a general rule, but what about with an empty trailer that weighs 1000 lbs? I know obviously if it's hunting for gears I would need od off but I doubt it would be hunting gears. I could carry 3 330 lb people in the bed and I wouldn't take od off.

Flatbed landscape type trailer 6x12

 

Just drive it.

If you notice excessive hunting in and out of OD at highway speeds, then turn off the OD.

This ain't rocket science, after all, so don't over think it.

 

If it will hold OD with the TC locked on the highway, no reason to turn OD off. If I were towing a lot heavier than that, then I'd turn it off.