If jiggling the screen unit makes it work, more than likely the cause is a loose connection (such as a cracked solder joint) in the screen unit. A competent electronics repair place should be able to fix that fairly readily, assuming they can find it. If you're reasonably handy with a soldering iron, reflowing the joints for through-hole parts would not be a bad idea, bearing in mind of course the high voltages involved with a CRT. (They can store a high voltage charge for quite some time in the flyback circuit after power is removed.)
It may reasonably be a connection to one of the cables at the screen or a faulty cable at the connector. Jiggling the wires should show that if it's the case.
