Evinrude 1978 -1979 have a capacity discharge ignition unit as the control for the spark system
it runs wires to an ignition coil
so I would be suspicious of that unit
check all connections for corrosion and bad connections
I typed in electrical schematics for 1978 evinrude out board engine and found a site --www.maxrules.com which in the list of schematics has 55hp 1977-1978
press on that and you get a schematics of the wiring diagram evinrude 1978-1979 55hp
now I am aware that you state that yours is 35 hp but if it has 2 cylinders then it is a fair bet that the wiring diagram will be the same
any way there are plenty of other sites that may be of benefit
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