On my 175 EFI Mercury the red wire comes from the battery, via the starter solenoid, through a 20 amp fuse to the switch at the helm. From there power is made available to the instruments, ECM, trim/tilt motor and starter motor. I think this is conventional wiring and yours would be the same, or similar.
Here is a link to a Mercury maintenance manuals. A wiring diagram of sorts should be in there for your motor. See page 2B-25.