hello Chris,
I`m not sure were talking the same kind of tremolo here.
This tremolostop is not in line with the reed stops.
it`s moved more towards the bellows, and in the middle of the instrument.

I`ve added the link to the picture.

I have never seen anything like that before.

My guess:
The accordion has three holes under each flapper and that is why the three are up close to the faceplate. If you ever have looked in a Cajun accordion and noticed the middle two reed banks you would see them upright and "back to back" BUT each of the four banks has its own unique hole in the face plate, in other words--four holes, one for each reed bank. This one has only ONE hole in the faceplate for the TWO middle stops. The stop further back controls whether or not air is allowed to flow into the second set of middle range reeds that is slightly off-tuned to produce the tremolo. This means that the offset stop would control holes BETWEEN the two middle sets...the "dividing plate" between the reed blocks. The offtuned set would not have its own outside hole in the faceplate. When you open the offset back position stop, it would allow air to also flow into the other side of the middle reed block. This would explain why the reason for the positioning of the offset stop. This configuration would emphasize the tremolo effect a bit more, perhaps. It is similar to a "CELESTE" stop in a pipe organ. The off-tuned ranks of pipes provide the tremolo.

The only other way tremolo effect is produced on organ is a fan-like contraption that agitates the air in the box, but the fan-deal is run by electricity, and doesn't seem feasible on accordion. Or perhaps is has a gated fan-like system run by the accordion's own airflow--kind of like the ball in a referee's whistle that agitates the air-flow.

But knowing that accordions are so kin to the harmonica, and knowing how tremolo is produced with tunings in harmonicas and accordions to this very day, I am sticking with my first guess.

Somebody buy this thing and take it apart! How much is 25 pounds?

Just short of $50.

Did you notice how the bellow box is somewhat deeper on the keyboard side?

I hadn't noticed it before, but you are right. Maybe there is some sort of air-agitator contraption in the right hand side; I mean, some of these old instruments could get pretty strange. I don't know why else there would be such a difference in width between the two end of the accordion. I am more intrigued than ever!

remembering the sound of the instrument, it could very well be a gated fan, like Chris guessed.
It sounds a bit like a Lesleybox on a Hammond organ,

On further thought, two problems with the fan guess:


1. Wouldn't the fan have to reverse direction with the bellow changes? The air flowing into the the accordion would turn the fan one way, air flowing out would turn the fan the opposite way. Seems way too clumsy to me.

2. The draw notes "suck in air" from outside the accordion and would not be as affected as the push notes which uses air inside the bellow.

I'm sticking with the "hidden reed block" theory with the back stop operating airflow into the off-tuned reed set.

I just couldn`t wait, so i sent an email to the man mentioned earlier on.
He actually owns and plays an instrument like that.

when he unveils the secret i`ll post it here

I wanna believe it may be some kind of tone chamber.