There are a couple different versions of this truck that changed during the years. There are a couple DP40 models that show up and a couple of DPL40 models... i've looked through all of them.

The best i can tell from the wiring diagram for the diesel model is this 'relay' as you put it does get a positive signal from the same circuit as the battery positive circuit on the alternator which comes from the battery positive off the battery, the diagram shows it tied into that circuit. The diagram is calling this the engine stop control timer. It looks to have a 4 wire connection also.
The way the diagram shows it there is a 3 wire connector and then a single wire connector all connecting to this device.
Would that sound like what you are dealing with?

the part number for this part is 16A1111001