On his most recent tax return, as he has the past 25 years, Vice President Al Gore lists a $20,000 mining royalty for the extraction of zinc from beneath his farm here in the bucolic hills of the Cumberland River Valley. In total, Mr. Gore has earned $500,000 from zinc royalties. His late father, the senator, introduced him not only to the double-bladed ax but also to Armand Hammer, chairman of Occidental Petroleum Corp., which sold the zinc-rich land to the Gore family in 1973.