OK still not making clear. "Steady" doesn't tell me what you mean..................... The voltage "surface charge" on the battery may be fooling you
(Did you run the continuity checks?)
Try this:
1...With everything hooked up normal, confirm what it is doing voltage wise, running fast, so I'll assume "high" but post the battery running voltage
2...If the voltage is high, above 15V, pull the blue wire off and turn on the headlights, continue to run and post battery voltage for at least 1 minute. Battery voltage should drop to 12 .....something.
3...Then, Unhook the green and hook the blue back up, and continue to run long enough to see if the voltage climbs high again.