First off, do research on how to protect yourself and safely work on CRTs. You are poking around in parts that can and have killed people.

Breaking down of the flyback transformer allowing arcing is a common failure point in old CRTs and can cause the clicking issue you heard.

Give this video a watch, it's long at almost an hour, but it gives a great break down and explanation of how CRTs work. Once you understand how the entire system works together you can start testing the various sub systems to locate the points of failure. It's very possible and likely multiple things have broken down overtime. https://www.youtube.com/watch?v=aWVE3z1ZRtg

Will give it a watch. And I do know that you can die if you are not careful.

I am a low hanging fruit tube meddler of some years but no great intensity, I like the guides at repairfaq.org for explaining things well. I would also tend to suspect flashover from the flyback as the cause of the described symptom.