Hi Manuel and
to the forum.
Here is the wiring layout for the MPIII, which should be the same as the Smart Pie III:
If your wiring is the same as the later MPIII/SPIII shown above
do not connect C3 to B4, as the yellow wire (B4) will be supplied with full battery voltage when the horn button is pressed.
To activate reverse, you simply join the Blue and Black wires
(C2 and C3) on cable "C" using a simple on/off switch.
If you want to use the switch mounted on the throttle unit,
you may need to rewire the switch inside the throttle housing so that it switches the light feed to ground (instead of battery +) and then simply connect C3 to the B1 lighting feed wire to complete the reverse circuit.
The thumb throttle can be dismantled relatively easily to access the switch wiring
(check out this post for more information) but the twist throttle is a bit more complicated to dismantle
(Check out Tommycat's post on electricbike.com for full details).
I am somewhat puzzled by your description of the four pin plug
(Plug "A") as you appear to have mirrored all of the connections
(compared to the above diagram) and the horn switch would be unusable if there was "NO PIN" on connector A3.
Regarding Plug "D" that is used for the speedometer display and USB programming cable on MP4 and MP5, on the MPIII harness that I tested when I drew the MPIII wiring layout diagram shown above, pins D2, D3 and D4 were not connected to any other wire on the harness and therefore could not be used for any purpose whatsoever.
On the MP4/SP4 harness this connector had the Transmit and Receive wires added:
The MP5/SP5 harness also added a +5V feed to this connector
(presumably to power the Bluetooth dongle):
I seem to recall that some MPII harnesses were cofigured slightly differently at the factory to allow the throttle mounted switch to activate the reverse function instead of switching battery voltage to the LED light.
Alan