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The coils are 580118. They have been superceded by 582995. They are available from the usual parts vendors. I’ll try to find a link to the parts list. Your motor is a Gale 5D10.
That is a standard magneto used by OMC(makers of Evinrude, Johnson and Gale Products) from 1951 through 1991. The coil cracking is a known problem. Coils are available. The most common one is made in china and has problems with the fit of the coil core laminations. the fix has been to remove the coils and install them on your old laminations. Your Sea King is a Gale product, probably a 35GG9015A which is Gales model 5D10. Since you are a member you can look it up on the Gale products parts list I have posted on my Dropbox account listed on our Technical Discussion page in the members only section . . .