Well, I finally had success today! Every aspect of the running lights and signals are working perfectly. And it took all of 10 minutes to do it!
So what did I do?
Last Friday, as I was trying (unsuccessfully) to fish new wire through the tiny hole and rubber-grommet-filled interior ribs, I decided to run an external wire to the new running light that wasn't working. I just wanted to see it glow! BUT IT DIDN'T. In fact, when I took it off of the unit and connected to my battery charger, it shut down the charger!!! Yep. BAD BRAND NEW LIGHT.
By the time I figured that out, I needed to leave. This morning, I tested one of my other new lights and IT worked. So, I connected all of the wires that I had disconnected in an effort to bypass my short, installed the new, new light and the whole system worked! lol
I thought I remembered someone suggesting this initially, and I found that TG Twinkie suggested something really close. I should have taken every bit of advice seriously! ;-)
Thanks for all of the input.
I will likely switch to LED at some point, you can bet I'm gonna check every one prior to installing! LOL