I just did a google search for “johnson outboard starter switch plate” and found several pieces out there. Not the exact same as your picture but here’s another one with push button start and choke:
https://www.ebay.com/itm/123737773709
You can also place a want ad on the Classified section of this site – perhaps another member has one laying in their stash of old parts.
Bob
1937 Champion D2C Deluxe Lite Twin
1954 Johnson CD-11
1955 Johnson QD-16
1957 Evinrude Fastwin 18
1958 Johnson QD-19
1958 Johnson FD-12
1959 Johnson QD-20
“Every 20 minute job is only a broken bolt away from a 3-day project.”
"Every time you remove a broken or seized bolt an angel gets his wings."
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