Roland BK-7m Backing Module
manuals
Roland A-49 MIDI Keyboard Controller
manuals
After thoroughly reading the manuals, I have the following ideas
Pre-recorded organ sounds
It sounds like the Roland BK-7m module might have some pre-recorded organ sounds that include variants with a fast and a slow rotary speaker sound. For those pre-recorded organ sounds, Control Change 16 might toggle between the fast or slow variation. (In the Roland BK-7m manual, page 54 mentions the "C1 parameter" which has a different effect depending on which sound is selected, for example, "it may [...] switch between the organ samples with the fast and slow rotary modulation [...]". Later on, page 68 mentions CC16 is a "general purpose controller that allows you to influence the C1 parameter".)
The Roland A-49 controller keyboard has buttons called S1 and S2 that can be programmed to send a Control Change message for any controller number 0 to 127, but they can only send a controller value of 127 or 0, either on press (127) and release (0), or on first press (127) and second press (0). In the Roland A-49 manual, page 31 explains how to set this up.
Try the following
To set up the S1 button to send Control Change 16 with a value of 127 on the first press and a value of 0 on the second press, press the following key sequence:
FUNCTION
S1
CTRL CHANGE
NUMERIC ENTRY 1
NUMERIC ENTRY 6
OCTAVE +
On the BK-7m, try selecting one of the organ sounds, perhaps "Rotary Organ", then see if pressing S1 on the A-49 changes the sound between a fast and slow rotary speaker sound.
Audio effects
The Roland BK-7m also appears to have audio effects (called "multi-effects" or "Mfx") that can create rotary speaker effects on any sound.
In the BK-7m manual, page 55 lists the Mfx types. I see three with "rotary" in the name:
Mfx type 9 is "Rotary"
Mfx type 57 is "VK Rotary"
Mfx type 83 is "Vib-Od-Rotary"
Pages 107 and following list the parameters available for each Mfx type. Each "rotary" type has an overall slow/fast speed parameter:
Mfx type 9 "Rotary" has a parameter called "Rotary Speed (Slow, Fast)"
Mfx type 57 "VK Rotary" has a parameter called "Speed (Slow, Fast)"
Mfx type 83 "Vib-Od-Rotary" has a parameter called "Rotary Speed (Slow, Fast)"
If you want to control one of these audio effect rotary speeds using a MIDI message, in the BK-7m MIDI Implementation document, pages 17 and onward seem to show that the Mfx effects can be set up with System Exclusive commands and then maybe certain functions assigned to Control Change messages (?), but the description is too brief for me to understand fully how they work, it would take some experimentation.
Be aware that the A-49 can't send System Exclusive messages, so it seems like this kind of control wouldn't be possible using only the A-49 by itself. Perhaps you would need to experiment with sending the System Exclusive messages from a computer to the BK-7m to see if you could eventually assign one of the slow/fast parameters to a Control Change message. Then perhaps you could assign that Control Change message to the A-49's S1 or S2 button.