I hope that someone can help me as I have not been able to get an identification for this plant in more than 50 years. I am unable to get a full shot as it is currently meandering through other plants but I can describe its growth habit. It grows in both shade and sun but, when in shade, the leaves become smaller (about 80% of the size shown) and darker, and the distance between the leaf nodes shorten. When planted on its own, it grows about 24-30" tall before it flops over. If it has to compete with other plants (as it is currently doing), the stems can easily become 5-6 feet long each if not longer. At a previous home, I used it as a ground cover and it filled a 750 square feet area in under 6 months so it is fairly aggressive in growth. I did keep it "mowed" to about 18" high using hedge sheers once per month and it became extremely thick. It was not, however, what I consider invasive as it never appeared elsewhere in the garden*. It is flexible in terms of water but looks its best with regular water but it is fairly drought tolerant and does just fine with a monthly soak. It is evergreen and blooms throughout the year and has an alternating leaf structure. Both my mother and I have taken cuttings to various nurseries over the years but no one has a clue (other than "some type of wandering jew"). Here are some more photos - some of them have comments added:
Any help would be appreciated!
* I was saddened that I had never taken any cuttings of this when I moved years ago as it was a reliable, rugged, carefree ground cover. Oddly enough, after it had been absent from my garden for 20 years or so, it popped back up 2 years ago. I believe it rode in with an unknown iris from my mom's house although she does not actively grow it either (and the iris piece had been at my home for a couple of years before this re-appeared). Perhaps it was a stray seed that had a very long dormancy period or ???.