Re: 1959 johnson sea horse 35 hp
Sure. When it's running, you should see water and exhaust coming out of the exhaust relief port on the rear of the leg. The amount of water varies with engine speed but should be a goodly amount.
Note: You must have the leg immersed in water several inches above the anti-ventilation plate for the pump to work correctly. Often, people testing these outboards in a barrel don't have them deep enough.
If this outboard is new to you, you should replace the water pump impeller before using the outboard. Odds are you don't know when it was done last and, if the outboard has been sitting, the impeller will be brittle and prone to disintegrating.
Great outboard, by the way! Once you have it all sorted out, you'll fall in love with it, I guarantee. You may have to replace the coils in the magneto, though, if that has not already been done.