My wiring drawing shows a couple things for you to check out...

The starter signal wire also has a connection to the main relay & ECU. It looks like the fuel pump relay (within the 'main' PGM-FI relay) is grounded thru the ECU. Apparantly that's so the immobilizer can shut off the fuel pump.

When running, the pull-down coil of that relay is energized thru a dropping resistor. But it's also connected to that starter signal wire you're looking at. Apparently the starter signal can energize the fuelpump relay faster than the ECU can wake up & trigger it.

There's a diode (inside the main relay) to prevent back-feeding that wire. Maybe that's failing. But more likely Honda figured that back-feeding a low voltage (probably with a high impedance) wouldn't hurt the starter motor. I bet you'll find if you draw any current from that 5v wire, the voltage will drop right off. You must have a high-impedance input of some kind that gets triggered with very little current.

You must have tapped that wire between the ignition switch & the starter-cut relay. P & N are the 2 gears where the starter-cut relay pulls closed. Then you get the backfeed. Any other gear, the starter-cut relay is open, and the backfeeding is only seen at the starter-end of the wire.