Finding a Stick Pin End Closure

Try a craft store like Pat Catan's or Michaels in their jewelry making section.

You can try the back of a stud pierced earring; Use the end of another stick pin and "share" between both; OR in a pinch-- the eraser of a pencil will work quite well.

A professional jeweler may have some/something similar on hand.

You can use a small part of a pencil eracer for the end of your stick pin.

You could try a pierced earring back. You know, the clear plastic kind that are used on the bent wire posts.