Trouble Hooking Up Trailer due to "Gear Slack"????

Shifting into neutral or stopping for a few seconds longer won't remedy the problem. The pawl is essentially a pin that engages between the teeth of a metal ring. The ring is not free spinning and connected directly to the output shaft. This means that if the wheels aren't turning then neither will the ring. This is why shifting into neutral or keeping your foot on the brake for longer won't have any effect. Once you're stopped, the ring has stopped moving. When you put the vehicle into park, it engages the pin into one of the slots between the teeth.

Often times the pin engages directly on top of a tooth. The vehicle then can roll anywhere from a few inches to a foot before it actually engages the pin into a slot. It's possible that the additional roll can build up enough force to cause the pawl to skip a tooth or break completely once it's engaged. To prevent this, you should set the parking brake before shifting the truck into park. That way you know the brakes are holding back all of the weight of the vehicle and not the pawl. This is especially true if your are carrying a load or towing.

Another possibility that could cause similar symptoms is worn U joints. The additional play in a worn U joint will allow the vehicle to roll back and forth even though the pawl is properly engaged. If multiple joints are worn, the roll is magnified. Doesn't matter if it's the pawl or the U joints, setting the parking brake will prevent the vehicle from moving.