Model number and/or horsepower would help. Sears sold motors back then from 3.5 to 45 horsepower and not all made by the same company. The first 3 digits of the model number will identify the maker.
Elgin was a brand name used by Sears on it's marine products. Just like the motors many different companys made their boats. As JbCurt00 said a parts list never existed for those boats even back when they were built.
Any chance you can post a picture? Is it on the control box for the throttle and gear shift or on the dash? I can think of a couple of things it could be for but would just be guessing. What is the motor on the boat now? I know with a picture or two someone on here can tell you what it is. The first thing that comes to mind is for an electric choke but that is a wild guess without more info.
There is a chance, that if you can find a xxx.xxxx format model number, it may actually pull something up in Sears parts direct. Not information you could use, just neat if it worked. Sears kept great records that I can pull up IPLs for a 1968 garden tractor and have even gotten parts
