I'm just guessing here but it sounds like the car is using a VSS signal to disable the starter while its in motion via the neutral safety switch. The easy fix for this would be to run a wire from the starter wire at the ign switch (thick yellow wire) straight to the solenoid (fused at the connection made at the ign switch for safety). Keep in mind that this will effectively disable the netural safety switch on the vehicle and will then allow it to start in gear so do that at your own risk.
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