If the person is male you can ask them:
Did you dodge the draft?
Did you serve during the Vietnam War?
What was your reaction to the termination of the Selective Service System?
For any gender:
Were you gaga for the Beatles or the Stones?
Have you ever seen the Doors, Jimi Hendrix, the Cream, or Janis Joplin in concert?
Were you a hippie, or if you weren’t, what was your opinion of them back then?
What were your reactions to the assassinations of RFK and MLK, Jr.?
What colloquialisms did you use back then, if any?
Did you use words like far out, groovy, boss, bitchin’, or out of sight, for example?
Did you use any nicknames for law enforcement, such as the man, the pigs, the fuzz, etc.?
Did you freak out or do you know anyone that did when the USSR launched Sputnik?
Do you know anyone that used thalidomide?