@sofastudios, did you get this issue resolved? I was curious because I've had a line exactly like yours twice now on my 21,5" 2011 iMac display and both times it disappeared by itself.
The line was positioned just like yours, a quarter in from the left side of the screen. It changed color depending on the background (on a white background it looked yellow and on a dark background it looked blue) and it was not visible on screenshots. The first time it appeared a couple of years ago, when I was still on Mountain Lion, and I tried everything I could think of, performed resets, reinstalled the OS and what not, but after a couple of weeks the line went away by itself. The second time it appeared this June - it showed up over night on the exact same spot like last time and stuck with me until last week (it was just gone one day when I woke up my Mac).
I just wanted to chime in here to share my experience. Back when this happened to me for the first time I was looking for solutions online and all the posts I found basically said "well, hardware failure, that's it, nothing you can do..." and I was close to bringing the Mac in for repair. But, luckily, I had too much work to give the Mac up and a couple of weeks later the line was gone. This time it took a bit longer for the line to disappear, but I just waited it out 😉