318 Engine stumble

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To start with. I don’t think the module is hooked up backwards.
The picture shows how it’s hooked up. The terminal pins are different sizes. The female side on the plug matches the size of the male side.

The green one is smaller.

I’m headed in the right direction to sorting this out. I definitely didn’t expect it.
I ses what you mean on the terminal sizes. But that does not mean the green and white wires were not swapped when crimped. Or the pick-up is reversed internally (color code on wires backwards like AJ sez). SOMETHING appears to be make the ignition firing way out of sync with the rotor position.

What distributor/HEI kit is this? Is there any documentation with this that would show the pickup colors into the module?

Damper OD is something like 7.2 or 7.3". Some aftermarket ones vary a tenth of an inch or so from stock. If desparate, a big block Chevy tape is pretty close and will give about 1-1.5 degrees error at 40 degrees.