Starter solenoid PN

Good morning and Happy Monday. Set the popcorn aside ( for a moment ) please.

Starter Relay is confirmed to be wired correctly. Ignition key switch is verified to be wired correctly. Alternator has all the connections right and tight as well as the starter. Boat starts but will not turn off. For some history, I am not the original owner of this vessel so I do not know what has taken place over the years with it's wiring nor repairs completed. That said, I did come across something of interest. Previously I found (2) wires going to the key ignition switch going to the "I" terminal - a Purple one and a Light Purple (Lavender maybe Pink?) one. I traced the Light Purple one back to the Safety Kill Switch located at throttle area.

Now, this Light Purple wire is GIVING me 12v from the kill switch side. Is this normal? Where is it coming from?  So, I disconnected it from the other Purple wire and my dash lights are now working as they should. That wire is still sitting live wrapped in tape under my dash. Where is that wire supposed to go? and Where is it getting it's power from? Hmmmm

I'm ordering (2) new Fuel Relays today per your previous advice - that might be a solution and will check a box to eliminate any question there.