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Q1: what is the OEM part number for an outboard engine ignition key switch that was used on a Boston Whaler 2004 190 NANTUCKET?

If you want to buy the ignition key switch as a Boston Whaler part, contact a Boston Whaler dealer who specializes in parts, such as TWIN CITIES MARINE in Wisconsin, now doing business as BEACON MARINE/Twin Cities: https://www.beaconmarinellc.com/

Or, contact your local Boston Whaler dealer.

Most likely the ignition key switch is part of the engine manufacturer's OEM rigging. Since you do not specify the engine manufacturer, it will be hard to assist you.

For a Mercury 115 [engine you can] look up [the part number for a replacement ignition key switch at a resource described only as] Crowley marine. They have good diagrams. The exact part can be found.