Stepper driving Challenge

Wired up the first ULN2001 and it steps the stepper ... every 2nd step. I can hear the "pulse" on the steps where the shaft only jerks a tiny amount. If I drive pins 1 and 3 it works the the same; double steps so to speak. If I drive the other pair of pins it also works - but the other way ?! I've tried all combinations I think, and it still only does every other step or just to&fro.

Hmmm...I can not find any wiring hints. The stepper is a J262-135, "2 phase 6 wire". So I assumed to drive it like a 5 wire unipolar stepper, energizing one coil at a time. (I need not that much torque, the holding force is 1000% over the need for holding a clock hand :-) ) Yes, I know it is a 24V and I am only driving it with 12V, that shouldn't matter. I have verified coil connections with the Ohm meter

My suspicion is that the opposite pairs have to have opposite polarity; (the coils are still unipolar) that means the ULN2001 circuit is useless. I try to test that with some switches on a breadboard. I could wire it as a bipolar 4 wire and use a normal stepper driver, that would mean redoing the shield (here shown partially completed) and buying drivers

Ideas?

Other news

An early version of a program, that will drive the motors, with rudamentary animation for the while being, has been completed.

The mechanics of the gear needs revising - motor mounts and gears get in the way of each other. Just details, not a showstopper. 3D prints are cheap, fortunatly.