GalaxieX ---- As always thanks for your help. Your posts led me to do more research which led me to this 62 Galaxie T-10 on Ebay. My 63 Gal was built at the end of 62 and I believe the Ebay picture below would be my T-10 also.
This picture would seem to explain why the gear oils drip position always favors the driver side close to back of the "engine". The contour of the tranny case would guide the oil forward on the drivers side letting it finally drip towards the front of the tranny. It will be interesting to see if the hole is just completely open or what. The nylon case vent picture you posted is probably a viable replacement. What do you think ???
Your pic above shows the stock metal cap vent.
The tranny pic I posted shows the vent missing.
There is a small baffle inside the case that is supposed to prevent oil splash leaking out the vent.
It doesn't always work so well...
The plastic vent is a common GM part.
If your vent cap is missing, it will def leak there.
You could use the GM vent... or.... raise the vent....
I had a customer with a race prepped T-5 and he used a special oil and overfilled the trans 1 quart.
It leaked out the vent during racing. (road course).
I got a metal fitting with threads on one end and hose barb on the other end.
Cut threads in the vent hole in the case.
Screwed in the fitting and he ran a hose from there, up the firewall, and stuck the GM vent in the end of the hose.
No more vent leak.
This kind of thing (raising the vent) is common in the 4X4 world to prevent water from going into the trans (and diffs and T-case) when mudding.