They are rubber shell Packard connectors. Grandfathers of the GM/Delphi weather pack connectors. If they're in good condition they won't break. If they break, they were in need of replacement. The shells are rubber and they deteriorate with age, heat, and/or sunlight. They develop cracks and get spongy/powdery. The Prestolite wire also deteriorates the same way.
I just get a good grip on each half and pull/twist. They can be bear. With the breakers I use a metal bar with a notch to restrain the outer boot a bit. The male pin is in the larger outside boot. On my M36 they just pulled apart in pieces and the wire was green and corroded inside.
The spilt wire should be the power feed and have 24V on it all the time. It's fed from circuit 10 which feeds the cab power. One breaker is generally the heater and the other will be the horn. I would start with the single side of the splitter and start checking for power at each junction. On my truck I ended up cutting that feed wire back to a point where the insulation was good and added a double pigtail, soldered on and sealed with marine glue lined heat shrink. That eliminated the splitter. I ended up pigtailing the wires out of the breakers as well. You'll also need to trace down where your wiper power is spliced in as that's generally not factory.