So what could be the answer is that Peter Pit was using a Jerry Benson Dancing Cane. There is no mention that Pit's cane was made specially for him, or by him. It could have been a agreement that he helps sell the canes by using his name in the ads. Who knows. Peter Pit passed away many years ago.

As I said, my cane has 4 sections, and Peter could have requested that it be small enough to fit in his case for travel engagements. This one does look like it was fashioned from a stick blind people use to use. The sections are expanded like the blind walking sticks. It does not look like one continuous smooth rod. The cane tubing is 8-16' and the flared tubing at the 3 junctions is 9-16".

If I recall correctly, Peter had an endorsement arrangement with Jerry. I know for a fact that it was not the dancing cane that Peter used most often.
He showed me the cane he used one time when I visited him to ‘borrow ‘ some special invisible thread that he used with his performance cane.

His preferred cane was made up of only three segments that screwed together to create the full length cane. It was lightweight and he stored it in a special pouch with pockets... (rather like the kind that holds a roll of wrenches). He had a huge cone of thread that he got in Europe... very thin and strong. He generously offered to let me take as much of it as I wanted, which was just a bobbin or two. I think I have just a little left now...

Here's a link to the original ad for the Jerry Benson cane/walking stick and a photo of the Benson cane in my collection folded into the four sections.
The ad copy says "a walking stick suddenly appears"--but the the way that the cane "appears" is more like a Walsh Appearing Table than a Walsh Appearing Cane.
https://www.facebook.com/photo.php?fbid=......BBEA9-RA

As JNeal points out, Peter Pit endorsed the Benson cane, but it was not the cane he preferred to use in his act.
You can see the cane that Peter used at the beginning of the "Peter Pit: Memories" DVD at the beginning of this youtube link:
https://www.youtube.com/watch?v=WPhlObwMCEc&t=11s
It looks to me like a classic black cane with white tips.

The rather sharp tip at the bottom of the Jerry Benson cane makes me think Benson may have designed it to resemble an Alpenstock--the kind of cane that people hiking in the Alps might use to ensure good footing.

----- Amado "Sonny" Narvaez
Note: I purchased the Jerry Benson Walking Stick from a used magic site. It did not have the "instructions by Ptere Pit" with it. I'd love to see the instructions that Peter wrote for it if anyone can send me scans of his write-up.

Although the use of canes in magic acts is waning... and there is a lot of advice here that I don't necessarily agree with... I do have to say that the best looking, lightest, professional cane on the market is sold here... http://www.wack-o-magic.com/dancingcane.html

No video, but 8 pages of instructions and a treatise on what many consider the proper use of the dancing cane. The late Eugene Poinc said these instructions are not only the best dancing cane instructions, but the best written instructions for a magic trick ever.

As far as the use of canes waning... a lot of people today, especially younger folks, probably have no idea what a cane -- as used in the dancing cane -- is. So to them it's probably just a stick.

Those canes were popular among "well-dressed gentlemen" for many years, from about the late 1600s to around the late 1930s or early 1940s, at which time regular use of formal wear began to fade out. Back then people knew what the canes were: not an aid to walking but a "prop" that rounded out your formal attire. Nowadays we rarely see white tie and tails except at diplomatic functions or the Nobel prize awards, or the occasional orchestra conductor.

I was fascinated by the dancing cane for years when I was a kid starting out, but it never made sense to me for a teenager to use a "prop" that was part of a white-tie-and-tails outfit, especially if I wasn't wearing one. Later, when I did my cards and doves act in white tie and tails, I did use a cane, but it didn't dance.

Oh, and BTW, I saw the Wack-o-Magic cane at Magic Live a few years ago. It was... well... awesome.

Xavier Mortimer has an amazing dancing cane routine that he performs with a broom. He teaches it, including how to make your own, on his wonderful Penguin Lecture.

What’s the minimum working range for the dancing cane?

If by "working range" you mean distance from the audience, the minimum working range for the dancing cane depends a lot on which cane you use and what lighting you perform it in. I've done the Wack-o-Magic Ultimate Dancing Cane indoors with the audience only a few feet from me.
Here's a youtube video of the cane performed at the Vanishing Rabbit shop:
https://www.youtube.com/watch?v=YBw1NsqN3us

As Michael mentioned above, you can purchase the Wack-o-Magic cane directly from their website:
http://www.wack-o-magic.com/dancingcane.html

----- Amado "Sonny" Narvaez