Homing sends the spindle to the left front corner. Y direction is front to back . X is left to right.
Despite the right Y stepper doing an odd reverse spin before spinning the correct correction, the homing routine waits for both Y limit switches to be hit before moving on. This squares the gantry each time the machine is homed. Any +Y move (jog or g-code command) proceeds correctly. All following moves with a -Y component make the Y2 stepper begin with a reverse spin before eventually spinning the correct way.
So I know something is wrong along the path from LinuxCNC through a parallel cable to the controller box. Both Y steppers should be getting exactly the same commands. The right Y stepper is getting (or just assuming) a +direction signal initially before then getting a correct -direction signal. Like any -Y signal after a +Y move gets there late. Sequential -Y commands proceed normally.
Probotix has sent a new controller with new parallel and usb cables. I'll know Monday if they correct the problem.