i'm not entirely sure, but i believe it's used by the chassis for timing purposes (it picks up the pulses of high voltage going through the core) it doesn't really carry any current, but its just having a small amount of voltage being induced to flow through it at the same time as the transformer is producing the voltage for the horizontal sweep of the CRT beam.
since it's at the same time, the components that are connected to it likely time the video signal to begin displaying at the the beginning of the scan so the picture is properly on the screen.
if it's squealing, i would think that maybe there is something whose solder is loose and repositioning things, made a better contact.