The water in my house (on a well, 35 feet deep) does somewhat the same thing, only much quicker. When it first come out of the faucet, it looks clear. But let it sit for 10 minutes and it turns red-brown. Kind of icky looking, and to think we drink this. But the water has always tested good, no bacteria or anything like that.
The problem is, it's the minerals in the water itself (which actually are good for you). In our case, the red (and I can imagine the pink for you, which is a light shade of red) is iron in the water. The stronger the iron content,the redder the water will turn, until it reaches a saturation point and it turn brown. If the water sits, it will begin to form rust stains (or iron stains) in your sink, bathtub, toilet, wherever.
Your water is sitting in the lines in your camper when you are gone, just like in our bathtub, it's not moving. It turns a reddish color. You start running the water and it flushes out and begins to appear to be clear again.
If you were to catch a glass of water and let it sit, I bet it will turn reddish-pink on you too.
There's nothing wrong with your camper, it's not pink antifreeze, it's the actual water.
Our rust in the water problem was solved when we ended up getting a whole house filtration system (
Kenetico), which runs the water through a sand filter and removes the minerals from the water. It runs on no electricity, back washes itself and even has a water softener ... no electricity at all. Except in very rare occasions, this took care of the rust and the red-brown occurring when water sat (in a glass or in a bathtub, or in the bowl of the toilet).
So, to test it out, get a glass of clear water and let it sit. See if it turns red. If it does, there's nothing you can do except filter your water.