It will differ a lot regionally, as stations made their own decisions regarding “local programming” in the early morning hours. As noted, some stations still do “sign-offs” today. However, I would agree that sometime in the 1970’s was when you were likely to find something other than test patterns at 2:00 AM somewhere on the dial in many parts of the country.
BTW, the “Indian Head” test pattern looked like this:
http://www.mediacollege.com/video/test-patterns/television/indian-head.html
It wasn’t universal though - my earliest memories are of living in the Buffalo, NY, vicinity, and I distinctly recall a test pattern with the outline of a bison.
Cable TV did not originally have it’s own programming intended to compete with the broadcast channels. The original idea, called CATV, stood for “community antenna television”, and was simply to bring reception to rural and small town fringe areas requiring large mast mounted antennas to pick up anything. You subscribed to the service and shared the costs of maintaining a big tower and a huge antenna on top of a hill somewhere. It wasn’t for a couple decades that it became an urban phenomenon, and it started occuring to people that you could create “cable only” programming and attract a large audience.
Another “when did it happen” - when did color TV’s start reliably adjusting themselves, and staying adjusted? I remember early color tv’s that had to continually be manually tuned to avoid watching purple or green people (of course, you could also derive extra entertainment by deliberately turning the newscasters green, etc). I would hazard a guess that solid state electronics had a lot to do with being able to design circuits that didn’t “drift” like old tube designs.
And of course, even for people that didn’t really know what they were doing, “tube testers” used to be available - if the TV set was on the fritz, you could take out all the tubes, go down to the TV repair store, run them all through the self-service tube tester, and replace the bad ones. Sometimes, it even worked, given that you actually remembered where each tube went.