The gear has a reverse spiral to direct the oil back into the trans. There is a o ring seal around the gear holder that may have failed. Sometimes the cable housing will develop a leak. The gear usually only gets replaced when damaged or a gear ratio change.Or the O ring.
Is there something special about a 1960 Chevy gear? Should find one on ebay if it's the common plastic type. Even a Chevy dealer probably still has 'em.