Knowing when to call a relative involves more than knowing their time zone. It also involves knowing a bunch of other details about their life, like their work schedule, if they have the kind of job where it is okay to call them at work if you keep it brief (eg overnight security guard who walks around once an hour and otherwise watches video feeds from cameras), whether they are a morning person or a night person, what non work activities they regularly attend (church, hobbies) and when they attend them, etc.
In practice, if you keep in touch on a regular basis, you don't actually need to remember their time zone at all. You can remember the correct time to call in relation to your own schedule: "Got to call Grandma as soon as I get home from work. If I wait until after I eat dinner, she will be asleep."
In actual practice, that's how most people seem to handle long distance relationships where they keep in touch regularly. (Or maybe that's just me.)
Plus, it's the relatively rare Luddite that you can only contact by phone these days. A lot of people keep in touch with long distance relatives via email, Facebook or text messages, all of which allow you to send the message whenever you feel like it without worrying if the other party is currently available for live interaction. If you can contact them via such a method, you can arrange an appointment for a live discussion by asking them when they would be available for such.