I think a lot of times they licensed the soundtrack for the initial broadcast(s) only. Home media wasn't a thing in the 60s for video.

Good point. Very unlikely it was licensed outside the UK even after home video started.

I think they showed it on PBS

As I understand it though, the typical way this would happen is through a new and/or separate licensing agreement (in this case for PBS, and for a different region, etc.)

The older programmes were typically exclusively BBC produced content - I can't think of any part of Connections that would be problematic for them. Surely with a new series of Connections having been made, they should have a look at making it available. It was a similar thing with their Oppenheimer series - fully available on YouTube and not on iPlayer.

Are you sure they didn't license e.g. theme songs, or backing music? That's often the source of problems with older content.

It's all fixable, but may not be considered worth the effort. Sometimes not worth the effort to audit even.

According to IMDB [1] 'Connections' was produced 'in association with' Time Life Films so probably some sort of clearance would be required from them ?

FWIW Time Life were involved in a number of distribution arrangements with the BBC, there's some details here [2].

[1] https://www.imdb.com/title/tt0078588/companycredits/

[2] https://en.wikipedia.org/wiki/Time_Life_Television#Televisio...