Mr. Jones,  I don't know much about fairground and band organs, but
in conventional pipe organs mixtures pipes are pipes ranks that are
speaking together but not selected individually one rank at a time.
They are selected at once as if it was a single stop.

The name, "Mixture", followed by Roman numerals indicating the number
of ranks composing the stop, comes from the fact that stop is made of
a mixture of ranks of different pitches and lengths.  As an example,
a stop called "Mixture IV" in a classical organ might be composed of
one rank of 12th [harmonic], another one of 15th, one of 17th and one
of 19th pitch.  When along the stop are notes involving pipes that are
too small to yield a strong enough tone to suit the ensemble, a jump
down to the next lower pitch is made but that jump is also applied to
the other ranks.  This process is called a "break".

Mixtures are not made to be played solo all by themselves.  They are
made to complement the palette of other stops so they are used in
conjunction with these.

(1) To simplify the description of Mixtures in ordinary pipe organs
we can say that they are compounded stops made of several ranks of
different pitch speaking together.

(2) The advantages or the goal of using such compounded stops is to
implement the colour and the power of the organ, adding brilliance,
permitting at the same time the distinct "voices" and melodies to be
heard clearly and followed easily by the listeners.

(3) About manufacturers of band or fairground organs using Mixture
ranks or stops in their instruments, I can't say since this is not my
domain of expertise.  If you were asking about regular theater organs,
concert hall or church organs, I would say that all makers are using
Mixtures in their production but not always; it depends on the style
and size of the organ.

Also to be considered here, Aeolian, and other makers of large
roll-operated pipe organs, did use Mixtures and other types of compound
stops in their production.

Gilles Chouinard
Laval, Quebec, Canada