Certainly looks like it. The native Lonicera sempervirens (which is the only other one that is a vine that I know) has more narrow leaves, often with a reddish tint.

Coral Honeysuckle is what I was hoping beyond hope that it would turn out to be. But I have noticed that the leaves and the stem don't match-up. The coral also doesn't have the long petioles(?) that I'm seeing on this one.

Well, thanks for your input, it's not 100% confirmation, but it's pretty close. Almost time to go yank out two vines and relegate the pots to seeding jobs.

Lonicera peryclymenum and L. caprifolium are vines and there are many others. This could be L p or L c but it could also be L japonica. I'd give it a little longer. Have you seen the flowers on your neighbour's? Google images for the three and see what you think. (But watch out, some are misnamed.) Lj has flowers in scant groups of 2 or 3 whereas Lp has a wheel shaped inflorescence of many flowers. Lj has black berries while Lp has red. L c has perfoliate leaves at the top of the flowering stems.

No, I never noticed any flower on her honeysuckle when it was in 'bush form'. I say bush form, but it turns out that there was a lone 4x4 in the center that I didn't know was there until all the honeysuckle had been cut down. According to her, her late husband had planted the vine some 10 years ago and trained it to grow up the the 4x4 where it then started growing on itself and formed the 'bush'. I asked her again if she remembered what kind of flowers were on it and she said, "Yellow, maybe white... I don't remember really."

I was surprised when she first told me it was honeysuckle, because growing up in SC I always knew when honeysuckle was blooming because it smelled so darned good and, as a kid, I would run around pulling blossoms and sucking on the 'honey'. So living across the street from her for two years and never realizing there was honeysuckle right in front of me kind of blew me away.

I thought I had posted this on this forum as well as the Name that Plant forum, but I have decided after a few agreeing opinions (both online and IRL), to pull the vines and let them burn out under the sun. "Yellow, maybe white" is not "orange, maybe red" so it's definitely not Coral Honeysuckle (which I wanted), which had already been decided (leaves were wrong). I'm going to wait until they're both dried out and completely dead before adding them to the compost heap.

Thanks for all the help.