John-Del wrote:

The fact that the line moves in that manner pretty much eliminates the display as a possibility, but it could still be a main board issue.

When the line appears, put up the TVs own menu. If the line disturbs the menu, it's a TV issue.

Hum seems to have been the problem. Now that you mention it,
there never has been a problem in the menu displays. I should
have thought of that.