Ok, what you need to understand is that how the transmission is controlled is not important, what is important is the result. I experience this in our Dakota all the time, and it uses a computer controlled transmission based almost entirely off throttle position and vehicle speed. When you go up a hill, it doesn't have the torque to maintain a constant speed, so as you give it more throttle it reaches a point where it decides to drop out of OD. This results in more HP from the same throttle position, so the vehicle will actually start to accelerate. As it build up speed, the computer eventually decides that OD is a good idea. It shift back into OD and the cycle repeats. The only way to stop this cycle is to switch out of OD.

The Fords work the same way. The computer uses a combination of TP, load, and vehicle speed to decide when to shift. There are points where you have enough weight that it can't pull a hill in OD, but the next gear down has abundant power. It will shift between the two gears repeatedly unless you manually shift out of OD.

 

I have a 1997 F-150 4.2 V6 2wd with 4R70W tranny and 3.55 gears, I routinely pull a 14ft trailer loaded with a Kubota B7500 Tractor with FEL and rear counter weights, The tractor also has calcium filled rear tires for additional counterweight, the total weight between trailer/tractor combo is probably a bit more than your Rhino and I hardly ever use the overdrive lockout button, occasionally when I encounter a steep grade I will use it but most times I do not need to use the lock out as the truck automatically downshifts to the needed gear, Your truck with the bigger V8 engine should have no problem towing your Rhino and you probably will not need to lock out the overdrive very often but it will of course depend on the terrain your are driving thru, On an open highway I maintain a constant 65 mph with ease and the truck does not labor. You will know when to lock it out or leave it alone, If the truck is constantly upshifting and down shifting while on open highway driving then you will probably want to lock it out, if it is pulling fine then leave it alone.
Val

 

This discussion has started to get somewhat interesting. My comment was based upon the 6L80E transmission which GM uses. It has a TCM for transmission control. The module is actually inside of the transmission case and rides in hot transmission fluid as hard as that is to believe. I don't believe Ford uses the 6L80E, but they may use a TCM. Initially there was the PCM which controlled BOTH the engine and transmission. As the technology developed the engine and transmission got their own separate controller specifically a ECM and TCM. Some vehicles like the Expedition and Escalade can have 30 or more control modules. It has gotten out of hand like a module for the vanity mirror on the passenger sunvisor. It isn't really important to the original question of "hunting" whether it is controlled by a TCM or a PCM. Overdrive doesn't have the torque needed for towing. You can activate the O/D switch or not during towing. You still won't have the torque needed to pull a heavy load up a hill or mountain which means you won't be in O/D either way. As far as "hunting" you need a range multiplier or a gear like 2 1/2 or 3 1/2 or 4 1/2 which you don't have to choose from so the controller(TCM or PCM) keeps "hunting" for the right gear to get the job done. It gets aggravating after a while, but there isn't much you can do about it other than get a tranmission with more gears.

 

Fords use a single PCM. It controls all of the powertrain.
JL

 

I have a 02 F150 with a 5.4 44.10 gears. I tow a 23ft travel trailer with no proplems. I tow with overdrive on and if I get in to a hill I just turn it off let it shift down get to the top and switch it back on.Trailer load goes about 6000lbs. If I know its going to be a hilly road I will run premium fuel.