Should I be using the manual gear switch when towing a 3,000lb trailer?
Agreed. Provided you have tow button, hit it and forget it. I can definitely tell a difference on the occasions when I forget to hit the tow button. The only times I’ve manually downshifted is heading down Deadman’s Pass in the winter and another beast of a decline in Pennsylvania. My travel trailer weighs 7418 lbs. empty so you should be fine in auto. I’ve got to get a photo of my Ram towing it, but the pic shows me pulling it with my old F-150.I just use tow haul mode and let the computer do its thing.