Sign, JOOC, what are you expecting to gain by using this circuit? In the original configuration, you are switching the coil current on and off with a mechanical switch. With the box, you mover that function over to a transistor, but you are still using the mechanical switch (points) to determine the timing. The only thing I see you might gain is increase life of the points.
To me it is like using a motor to drive a generator to drive a motor. No functional gain, just added complexity.
According to the instructions, if there is a ballast resistor, the power for the board needs to come before the resistor - basically any ballast resistor needs to be bypassed. If you are making all you connections at the coil/points, then I don't see how you can be affecting the horn circuit. And the coil should not /can not be drawing any more current than if the motor was stopped with the points closed. Double check the way you are connecting the unit.