That sounds like 60Hz interference with the CRT display. There are two prime causes of it, in general.
First, magnetic interference from a nearby transformer, electric motor or other machine. Does the line get more pronounced or less noticeable if you move the Mac around or rotate it? If so, the interference is coming from outside the Mac and the only solution is to move or reorientation the computer or whatever's creating the interference.
The other likely possibility is failing capacitors in the Mac's power supply, which may itself be part of the analog board (I don't know the SE well enough to say) . As the capacitors age, they both lose capacity and gain internal resistance, so they don't do such an effective job of smoothing out the incoming 60Hz AC power. The Mac's power supply is doing its best to give a stable output, but there comes a point when small 60Hz variations find their way into the output, which can affect the monitor in the way you describe. Replacing the capacitors isn't expensive if you're handy with a soldering iron and understand what safety precautions to take.
Those of us who live in countries where the power is 50Hz would see a disturbance on the screen flickering up and down 10 times a second rather than the slow-moving bar you're seeing. The movement of the bar on the screen depends on the difference between the local power frequency and the Mac's fixed 60Hz vertical scan.
Chris