Re: 1965 33 Evinrude Ski twin
That's the vent plug for the gear box. There is an identical plug underneath the nose of the gearbox, which is the drain plug. The vent plug serves to allow the oil to run out when you change it. It does this by preventing a vaccum in the gearbox, which would "prevent" (actually the oil will run out, but slowly) the oil from coming out the open drain. Replacing the vent plug after you refill an empty gearbox, also allows you to disconnect the oil tube and replace the drain plug, without losing much gear oil.
Your problem is most likely a defective crush washer. This washer should be replaced on both the vent screw and the drain screw, every time you remove them. Since many amateur mechanics don't do this, the screws tend to be the most common places where water intrusion into the gearbox happens.
Since yours in leaking oil out, you can be sure that water has been getting in. That means that you should immediately change the gear lube. When you drain the old lube, look for a milky appearance. You may also see "water bubbles" in the oil. I don't have a manual for a 1965 OMC 33hp, but my 1968 manual specifies "Type C" gear oil. The modern equivalent of this oil is "BRP Premium Blend," which you can get at any OMC/BRP dealer. The quantity required is 13.9 oz.
PS: I just noticed that I didn't read your post carefully. If the hole is below the cavitation plate, it would not be the vent and the other information given by R.Johnson is probably correct. I'll leave the above info anyway, just in case it is useful to you in regard to gear oil/gearcase issues.