Jeff,
I like the idea that the photos were taken on one of the NG logging railroads out of Lumberton. The Rio Grande and Southwestern ran from lumberton 42 miles south to Gallinas. It was constructed beginning in 1903 and completed by January 1906 which would work with the stated time of the photos from a trip in 1906. The photo with the engine has hand-hewn logs and could have been used on the logging road which could have still used link and pin couplers. The other photo also has hand-hewn ties except for the turnout which has milled ties.
Don