I think RichLo covered why this doesn't work. And yeah, that was the preface of my whole adventure here. If you leave these lights plugged into the cord constantly as the manufacturer suggests, it kills the battery very quickly. A new or near-new battery that would previously last almost the entire work week now will no longer last a whole night on a "full" charge. Permanently damaged capacity. That's what is behind my whole series of "new battery for the tow lights" posts recently - I had to change mine after about a year because I forgot to unplug it, and it's something that happens to my co-workers frequently, as well. So I replaced a whole whack of batteries for several of them.
Richard