Thanks for all these good suggestions. Believe me, in trying to figure this thing out, taking a 10lb hammer to it has already been considered!
Guest Jon, the photograph is almost like my instrument, the main difference being the black keys on mine are in 2s and 3s like a piano keyboard. Where the missing black keys would be, the switches stick out like mushrooms. The switches are marked '1A', '1B', '3B', '3A', '2N' and 'BA' (although the 'A's look more like upside down 'V's). The 1A switch is between the first
white key and the edge of the keyboard. There is a 7th switch marked '4' which is on the side of the bass end of the keyboard (i.e. at a 90 degree angle to the other switches).            
The instrument in the photo has 72 keys, mine has 74 of which only 52 are attached to a valve (22 keys (12 on the bass end and 10 on the treble end) are not attached to anything and do not
play). There are only 43 actual notes/valves on the treble side, so of the 52 keys, 9 are doubled to
the same note.
The actual notes are as follows (bass to treble) X = key not attached:
Black row: (switch 1A)-X-X-X-(switch 1B)-F#-A-(switch 3B)-D#-F#-A-(switch 3A)-D#-F#-(switch 2N)-C-D#-F#-(switch BA)-X-X
Long White key row: X-X-X-X-F-G#-B-D-F-G#-B-D-F-G#-B-D-F-G#-X-X-X
Middle (stub) White key row: X-X-X-E-G-Bb-C#-E-G-Bb-C#-E-G-Bb-C#-E-G-X-X-X
End (stub) White key row: X-X-D#-F#-A-C-D#-F#-A-C-D#-F#-A-C-D#-F#-A-X-X
From the photograph I could see the black key notes being (if the switches weren't there): X-X-X-D#-F#-A-C-D#-F#-A-C-D#-F#-A-C-D#-F#-X-X-X
I think this is some kind of arrangement to make the fingering the same in every (musical) key (like the bass buttons) but the logic escapes me.