The Serial Toggles mark the beginning of the "Gillette Adjustables" era.
Gillette only manufactured them in the 3rd quarter of 1955 and started selling them, making them the first adjustable razors that the company sold. There were no adjustables manufactured in 1956 and 57, so presumably the sale of these spilled over into those two years.

Unlike the later adjustables, although they had 9 divisions, they were numbered 1 - 5, with half positions and the indicator was a Red Dot instead of the spring. They have a few more unique features one of which is that when you swing the toggle one way it opens the doors enough to rinse the razor and if the toggle is opened the other way the doors are opened enough to change the blade. (See right most image of the second row)
I've since listed the differences between the various Toggles HERE.
There was also a Nickel plated version which is extremely rare.

They all have 4 digit serial numbers indicating that a maximum of 9999 were manufactured or planned on been manufactured. This ones serial number is 2526 and it was probably initially sold for the princely sum of $7,50.

The patent number is US2848806 (Click to see)

How does it shave?
I found it a bit more aggressive than the other Gillette Adjustables.
I've found that I like it on 3 for the first pass and dial it to 3½ or 4 for the next two passed and I end up with a great shave.
If I'm looking for a BBS shave I just add "1" to those numbers.

The Repair
When I bought this, the Ebay listing stated that the dial didn't move, so no surprises there.
Once it arrived, I soaked in citric acid for a few days hoping to dissolve the soap scum buildup but there was no change. It was stuck and needed to be stripped down and a freeish Saturday was just the day to do it.
I started very early and kept going back to the patent drawing so it took a while for me to strip it down. It's done its fair share of shaves and the internals were caked with soap scum. Once I had it stripped down, I left it soaking in a citric acid solution for a while and that loosened the muck enough for me to use a soft toothbrush to clean it.
When I started scrubbing, I broke the one internal piece and spend the next hour or so making a new one out of brass (it's the small ring just above the toggle in the left image below). This little ring is there to limit the start and end points of the adjustment dial and it needed some "fine turning". This was done with a needle file a little bit at a time.
I've since read that it was made in aluminium which tends to oxidise when leaving soap on it for extended periods. That would explain why it broke so easily. (Since reading that, I'm glad that I made it in brass)

I've added the third image below, which is a close-up of the new little ring. I started with a piece of brass rod which I centre drilled and outside turned to the right sizes. Once that was done, I parted the little piece and was left with the two pieces in the image.
I then proceded to hand file both the inside and outside until I had it fitting. Once that was done It was still a bit thick, so I carefully sandpapered it thinner to fit, and then did the "fine-tuning" mentioned above.

The last thing that I did before reassembling it was put black paint in the numbers and line markers on the adjuster dial and red paint in the two "dot" markers, one for the adjuster dial and the other on the toggle itself.

It was a bit fiddly getting the numbers vs clicks to line up with the top red marker, but other than that its easy to reassemble.

This has been confirmed before - They were made in the 3rd Quarter of 1955. A3 is on the middle plate and is hidden with the razor assembled. (Clicking on the images below will open a big version of them in a new tab)

Serial Toggle number 2526 back in service and reporting for duty...