It took some detective work for me to figure out that the alien motor is controlled by a pcb under the playfield that is not called out or documented anywhere in the BBB manual or wiring diagrams...
Here's the schematic that shows how your alien motor should be getting driven. Power comes from the power driver board on J16-pin9 (Yellow wire) and goes down under the playfield to the tube dancer motor (S30) and the motor control board in the center of the playfield (which uses the S31 and S32 controls to spin the motor).
The S31/S32 motor returns come from the same 7-pin connector back on the gray/black and gray/violet wires to J25 on the driver board. The transistors on the driver board open/close the S31/S32 circuits.
There shouldn't be any connection between J6 (the display board power connector) and the motor control board. Power should be coming in on the yellow wire from J16. Ground should be coming in from the black wire on J14.
Disconnecting J6 should not have any impact on the motor control board. You should check the power and ground connections going to the motor control board. If either power or ground for the motor control board is coming from J6, something is connected or wired incorrectly.
BBBSchematic (resized).PNGBBBMotorControl (resized).PNG