For power to the I terminal, you can see if any of those loose connectors have ~12V power when the key is on and not when it's off. If your Mikuni setup is like my '87, the fuel cutoff solenoid terminals are bundled into that multi-terminal connector block. You may wish to just cannibalize the old carb side of that connector, cut the wire pair at the cutoff solenoid, and splice onto that; one of those wires should get 12V switched current, and the other is a ground. You can tell which gizmo is the solenoid when you plug it in and turn the key, you should hear it click.
A relay is a switch in one circuit that's operated by electricity in another circuit. You want a NO SPST type (normally-open single-pole single-throw), which has 4 or 5 terminals: two operate the internal switch, which dis/connects power across the other two, or some NO SPST relays have an extra switched output terminal (called a "dual make" relay). When power flows across the control terminals, that energizes an internal electromagnet that closes a switch across the switched terminals.
Why use a relay? The electromagnet draws tiny current, whereas the switch can handle high current, so you can switch a high-current circuit with another one that's low-current, dodgy/unknown, or otherwise worth protecting. The circuit across the ignition key switch to the I and then P terminals may not be strong enough to drive the pump, or you may just want to protect your ignition switch and pressure safety switch by reducing the current demand across them, so we use that circuit to operate the relay, which in turn switches current directly from the battery (+) terminal to the pump.
This page explains and illustrates more about relays:
https://www.the12volt.com/relays/spd...ive-relays.asp
Here's the basic wiring you'll use:
https://www.the12volt.com/relays/relaydiagram47.html
...where terminal 86 will take the 12V wire from your old cutoff solenoid , 85 will take the old solenoid (or any) ground, 30 will take a fused line from the battery (+) terminal, and 87 will go to the pump. If you get a dual-make relay with an 87b terminal, that allows for another trick you can do in a pinch: swap the wire from the 30 to the 87b terminal for constant power to the pump -- unswitched, so be sure to undo that swap once you reach your destination!
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