I can't see where it comes from, but my trailer has a similar faucet near the city water inlet. It is just a cold water outlet. In my trailer, under the bathroom sink there is a check valve in line with it and a valve bypassing the check valve. I think I figured it out. The check valve is above the water pump pressure but below typical city water pressure. With the bypass valve closed, the outside faucet works when connected to city water but doesn't work when boondocking using water out of the tank with the pump. With the valve open the outside faucet always works.
“You cannot reason someone out of a position they have not been reasoned into"
Al, K5TAN and Missy, N4RGO WBCCI 1322
2002 Classic 30 Slideout -S/OS #004
2013 Dodge 2500 Laramie 4x4 Megacab Cummins