Yes, if I move the horizontal hold left while retaining sync, the picture moves left very slightly, and so does the line. The line is also minimized when I adjust the fine tuning for less sharp detail.
When that photo was taken, I was receiving a broadcast from my in-house transmitter (Blonder-Tongue agile modulator) on rabbit ears. Haven't looked for the phantom line using another source yet, but I'll do so tomorrow.
Meanwhile, I'm glad I decided to pull the safety glass and do some cleaning. The inside of the glass was almost as grubby as the CRT face. I have never seen a screen & glass quite this dirty.
Phil Nelson