Like Rich, I do not have the Tailgater version. I usually use my 11# tank, only because of the dog's tie-out, so I tend to cook away from the TT. The hose works on the smaller units.
You do not mention what you have for a camper. Just an FYI on BTU usage;
12K BTU - 17" Blackstone
24K BTU - 22" Blackstone
35K BTU - Blackstone Tailgater
12K - 34K BTU - Furnace, most seem to be around 20K
8.8K - 10K BTU Water Heater 6/10 gallon tank
1.4K BTU - refrigerator
6.5K BTU - Stove - Back Burners
9K BTU - Stove - front Burner
? BTU - Oven
If you are running the Tailgater, furnace, water heater (BTU Range of 35+12+9=56 to 35+34+10=79) at the same time you could be close to maxing out your propane tank's regulator's maximum flow rate.
Propane tank Pig tail connector color represents the capable flow rate in BTUs
70K BTU - Black Propane tank plastic nut - typical on all RVs I have seen
1XX BTU - Red
200K BTU - Light Green
500K BTU - Dark Green
I upgraded the pig tail on my a manifold tree with my 11# tank, to the light green connector. The LP shop did it quick and was cheap.
Hence, I would be concerned about using it on the quick connect without upgrading the propane tank flow regulator (not pressure, but flow rate).