I bought two plants at Lowe's (which is walking distance, but it still doesn't make them native) a few years ago, hoping they'll fill up this part of the fence. They've gone high but not spread out too much. It's pretty shady in this little corner of the yard. They bloom white and yellow, but not right now.
There used to be honeysuckle around the outside a round lecture room at the college of education at the University of New Mexico. in the late 60's and 70's.