Having just redone a 1958 Mercury Mark 55, and not knowing how good or bad a condition yours is in, I suggest changing all the electrical components without question: Plug wires, plugs, points, the works. Then go throught the lower unit, get a professional opinion if you need to, and replace anything that is suspect.
Ebay is a great source for old parts cheap, many times unused and factory new. Oldmercs.com is a great sight, Bob Grubb is very helpful. Also strongly recommend getting the specific model manual, which Bob should have.
The good news is, your engine actually will share more in common with engines made over the next two decades than mine did, so parts availability gets a little easier.
"And look at Elias Wonder. Yeah, take a gander at that buzzard. Forty years ago he was happy, generous, charitable, tall, dark and handsome. Then he took up the fly rod. Now consider him. Uglier than fresh road kill. Evil-eyed, cantankerous, sullen, mean. An anti-social misfit that causes a groundswell of spleen wherever he goes."
-- Harry Middleton