If it drips with the shower head off, the problem is the spigot or some part of the valve that controls water flow. The shower head doesn’t in most cases control water flow. This could be a simple fix or not, but depending on the build of your shower faucet and how readily accessible it is will highly affect this.
Camper? Ice cream truck? Mobile dog wash mobile? Lots of things I can think of. I just wouldn’t want to deal with the maintenance lol.