Definitely go with an enclosed trailer if you are going to tow your Goldwing all the way to Alaska.
I have been towing bikes for 5+ years {first my BMW R80 RT, then the HD Dyna Super Glide and now my Indian Springfield}. I started with an open homemade stake bed {Harbor Freight}.
The next trailer was a nice Kendon folding single that due to the long overhang of our 24' Class C, protected the bike completely, not a scratch in three years and 20K+ miles but...
When I got the larger Springfield the Kendon was working way too hard so I upgraded to a 6 X 10' {14' overall) enclosed trailer. This for me is the perfect combination. The bike is completely protected {from weather, debris and bad guys etc.,} as basically, I'm traveling with my own custom garage attached.
In addition, the trailer has lots of extra room to swallow misc gear from the coach. My BBQ, firepit, LP cylinder, camp chairs, and rug just to name a few easily slide into the trailer. As noted, find a deal on a used trailer, use it and you can probably resell it for close to what you paid.
Here is a shot of our set up taken last January out on the Colorado River at Buckskin Mountain SP just north of Parker AZ:

This set up works so well, can't even see it in the mirrors and fully loaded {Bike, trailer and gear} it weighs just 2,220#. I just have to remember I am now 38.5' instead of the usual 24.5'.
:C