Welcome. Gerald. Sounds like you have a very nice combination there. I kind chuckled when you called your camper a "trailer" in you post. Folks in the Midwest and East Coast call everything from a motor home to a fifth wheel a camper, while I always think in individual terms, travel trailer, truck camper, pop up and so on.
Sounds like you are limited in space. Does the new "truck camper" have a rubber roof?
I'm asking because worse than the rain we get in the NW is the ultra violet degradation that roof will get if left out to the sun, but you mentioned you have a breathable cover and that's good for sun protection as well as keeping it clean.
I have never been a big fan of tarps, if you tarp a vehicle in a damp climate you also trap any moisture under the tarp. It makes sence if you have a vehicle/RV that leaks, but if it's not leaking I wouldn't tarp it. If you can't build a permanent structure because of zoning or set backs maybe a temporary structure like those metal framed tarp structures you can buy at Costco.
I'm so lucky I have a big garage that I take my truck camper off the truck, lower it onto a dolly and push it back into a corner of my garage. Good luck with your new purchase, now be sure and get out to Cape. Disappointment, Fort Stevens, or a multitude of parks along the Columbia River with your new unit. All the best, Hans