What is the instrumental soft rock song based on Taps that was popular in early 60s?

The song you're referring to is "Last Date," the instrumental composed and performed by Floyd Cramer, released in March 1960. It was an international number-one hit selling over one million copies in the US and became one of the best-selling instrumentals of all time. The song is based on the melody of "Taps," the bugle call used to signal the end of the day in military settings, as well as at military funerals.