Does the time difference between Auckland and Vancouver change during the year?

Yes. Because of daylight saving time the gap moves between +19h and +21h.

When is the best time to call Vancouver from Auckland?

Between 09:00 and 12:00 in Auckland, which is 14:00 to 17:00 in Vancouver.

Auckland is 19h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +19h and +21h during the year.

Auckland

New Zealand

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Vancouver

Canada

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A 9-to-5 day in each city overlaps for 3h. That is 09:00–12:00 in Auckland, which is 14:00–17:00 in Vancouver.

City	Time zone	UTC offset
Auckland · New Zealand	Pacific/Auckland	UTC+12
Vancouver · Canada	America/Vancouver	UTC−7

What is the time difference between Auckland and Vancouver?: Auckland is 19h ahead of Vancouver. This gap is not fixed: daylight saving time moves it between +19h and +21h during the year.
Does the time difference between Auckland and Vancouver change during the year?: Yes. Because of daylight saving time the gap moves between +19h and +21h.
When is the best time to call Vancouver from Auckland?: Between 09:00 and 12:00 in Auckland, which is 14:00 to 17:00 in Vancouver.