You're right, that green wire should only be live when the starter button is pressed.
Wonder if it has shorted to a live wire somewhere in the harness?
Either that or it's connected somewhere to something it shouldn't be connected to.
Ya gunna have to trace it back to where it's picking up the power.
Discconect both ends and trace back until you find the contact.
The blue wire is power to the dimmer, (Hi/Low Beam Switch) and white from the H/L switch is High beam, Yellow is Low beam.
There is no connection on the Ultima box for the regulator so I assume that it should be connected to where it was before. ?
The nuetral switch is a mystery, maybe one of the three wires is an earth. The Ultima diagram shows two terminals from the switch are bridged and connected to the 18 GA Yellow wire back to the box.
You will have to use a multi meter or test light to determine which wire is which and connect the one that earths out when nuetral is selected to the ultima box. The nuetral switch should earth via it's own housing, but if not, that will be why it has the third wire and that will have to be earthed.
This is the wiring diagram that I'm going on; www.ultimaproducts.com/18-533.pdf
Even though it isn't stated or shown, I would imagine that the Ultima box has it's own overload protection. You would hope.
It wouldn't do any harm to make sure, and at least install a main fuse in the Red main supply from the battery to the box, 30 Amp should be sufficient.
As a rule, anything that is connected straight to the battery should be fused, or protected by a circuit breaker, in case of accidents, wire chaffing, short circuits, and or the like. They protect not only the electrical components themselves, but also the wiring harness, battery, and prevent the possibility of an unwanted cremation, fire.
OK, so if the only wire to the battery + is the Red to the Ultima box, what you say makes sense, the fault could be internal.
but don't overlook the fact that that same Red wire/Ultima box also distributes power to the indicators, brake light switches, horn, headlight, and starter switch itself.
The problem does not neccessarily have to be in the box, it could be anywhere along the line from the starter switch (right hand controls) to the solenoid, where a short has occured from any of those other powered wires.
Make sure it isn't any of those before you take the box back as faulty.
Power connected to the box,
box earth lead connected,
the IGN switch is off ? (even if the IGN switch was on you would expect power to everything other than the soleniod wire)
but there is still power to that damn green solenoid wire.
If that's the case, as you suspect, then you would have to assume that something in the box is not right now.
If you open it up there is every chance that Ultima will not honour any warrenty.
Think it might be time to take it back and ask questions.
Everything appeared to be going OK untill the headlight Hi/Lo switch was connected. Ever since then, nothing has been right.
Edit note: Typing at the same time as you. hope als suggestion works,,, but why in the first place?