Dave,
The ford manual is titled "1965 ford trucks power transmission components Dana Spicer"
Best I can tell it is all Spicer stuff, with some of the smaller pto's being Chelsea.
The "Reversible Power Divider" is listed under the "Spicer Special Power Take-Offs and Gear Boxes" section. It has 1.25" shafts both in and out, so it is only intended to multiply the number of outputs from an existing PTO on the transmission.
I think that the most likely situation as described is a "split Shaft PTO" This would account for the main driveshaft turning while dumping. I also think that this type of pto is overkill for a simple dump bed.
By far the most common is a transmission mounted
PTO and a small driveshaft to run the pump.
It's possible that a tandem rear axle power divider was used because it was "laying around" Also possible that the Split shaft PTO was used for the same reason.
I think from here only a picture will give us an answer or more information.
Grigg