Sounds like a good mystery to chase!
And any good mystery gives us some clues to follow so let me check if what I see is what you have?
First is this the layout of the plumbing as you have it? I snipped this drawing from this link at page 224:
https://www.winnebago.com/Files/File...07/7wkp39k.pdf
It seems to show no valves, etc. between the vanity as I marked and the washer, so that leaves me a couple thoughts to try.
You were set up with water and getting water other places, with city water or pump on?
Maybe verify that you are getting water at the vanity (item 20) next closer to the supply.
The washer valves are open at 21?
Some possible thoughts. There are filter screens on many washers, right at the faucet/valve and they "might" be clogged?
Are you pretty sure you let enough run to clear the pink as that location is further down the line than other spots?
The nasty one to mention but works in my house is how well you know the machine. Any chance the wife would do it different?
Seems like if you get water at 20 but not 21, you are real close to the problem.
Good luck with the mystery!