What time actually controls
Time controls how much is extracted, not what. The order in which compounds leave the leaf is set mainly by temperature and by leaf surface area; time just determines how far along that sequence you get. This is why a longer steep on cool water does not reproduce a shorter steep on hot water, and why extending a steep to strengthen an under-leafed cup makes it harsher rather than fuller.
Rough ranges by category
Japanese green tea: 45 to 90 seconds. Chinese green and yellow tea: 2 to 3 minutes. White tea: 3 to 5 minutes, and longer than instinct suggests. Oolong western-style: 3 minutes. Black tea: 3 to 4 minutes, or up to 5 if it is going into milk. CTC and bagged tea: 2 to 3 minutes, and squeezing the bag does not help. Gongfu brewing is a different scale entirely — 8 to 30 seconds per infusion, extended gradually across a session.
Why the second infusion is shorter, then longer
The second steep of a multi-infusion tea is usually shorter than the first, which surprises people. The leaf is already open and hydrated, so extraction is faster; a second steep at the first steep’s timing will over-extract. From the third onward the times extend steadily, because the leaf has less left to give. A typical gongfu progression might run 10, 8, 12, 20, 35, 55 seconds — down, then up.
When a timer helps and when it does not
A timer is genuinely useful for short gongfu steeps, where five seconds is a large proportion of the total and the margin between excellent and bitter is narrow. It is much less important for a three-minute western steep, where thirty seconds either way is a modest difference. Taste as you go rather than trusting the clock: the leaf, the water and your preference all vary, and the number on a packet was written for neither.