First of all, welcome aboard, Great to have another '59er around. Second, yes, those are both original to a '59 trailer. As Terry mentioned, replacement lenses are available but the base hasn't been available for some time. You'll need to do all you can to keep them in working order. The one in the picture doesn't look too bad, I've certainly seen much worse.
Best of luck in your taillight efforts.
4CU 2699 / AIR 10 / TAC AZ-1
I'm haunted by aluminum.
Charter Member of the 4 Corners Unit.