I don't expect to get anywhere with identifying any of these, but you never know, so here it goes...
Cullen's TPiR had several closing themes over its run. The last one by Bob Cobert we know about, so that is not included in this discussion. I have found however that they used three prior themes, and some of them may or may not be commercial recordings or library music. I have no basis to identify what is what and hoped some of you could offer some input.
This is the recording of Sixth Finger Tune they used for the opening. In the beginning it was also used over the closing.
Here is the second closing from a 1958 episode. No idea who composed this or where it comes from.
Third closing, this from January 1960. I assume this was replaced by the Cobert music the next year.
Clicking on the above will take you to straight to the closing of said episodes for observation.
EDIT: Upon review again, I think #2 and #3 are the same recording, different parts of the track... no?