Bosco, when we went to the National in Montrose Colorado we learned a simple trick that worked for us.
We learned that KOA Campgrounds will store your truck/trailer for a minimal charge.
In our case we trailered to New Mexico, left the trailer there at a KOA, rode Colorado for the National, returned to the KOA, loaded the bikes on the trailer and headed for home.
You could call a KOA in Eureka Springs, and see if they have a secure area.
But a better deal is what Jeremy posted!
or, (thinking out loud) see if the Motel in Eureka has a secure area...
Ride safe, Ted