Your post raises a valid question: For calculating pivot points, when do the major trading sessions begin and end? And, specifically, which candles mark the open and close of the Tokyo Session, for calculating pivots in the London Session?
The short answer to your question is:
For trading the London Session, using Tokyo Session pivot points, refer to the session times for Tokyo and London given here – Forex Trading Sessions - BabyPips.com
That is, find the high price, low price, open price, and closing price occurring during the Tokyo Session (currently 11 pm GMT - 8 am GMT), and use those prices to calculate pivots for the London Session, which begins at 8 am GMT. Note that this suggestion ignores the Sydney Session, altogether.
Many traders do not ignore the Sydney Session. Instead, they combine it with the Tokyo Session into one long Asia/Pacific (APAC) Session. If you prefer doing it this way, then use 9 pm GMT as the open of the APAC Session (and use 8 am GMT for the close, as above).
If you’re not in the GMT time zone, then you’ll have to figure the corresponding times for wherever you are.
Here’s the long answer:
If you want to apply pivot points to sessions other than the London Session, you’ll have to make some additional choices regarding times.
For example, the London and New York Sessions overlap each other by 4 hours. So, if you want to trade the New York Session (1 pm GMT - 10 pm GMT) using pivots from the (previous) London Session, you would likely base your London Session pivots on the first 5 hours of trading in London – that is, 8 am GMT - 1 pm GMT.
Daily pivots are easier to manage than session pivots, because once you have specified the beginning of each trading day (typically 5 pm New York time), there are no overlaps to contend with. But, session pivots can be rationally applied and successfully used, as well, if you choose the session times in a logical way.
As to the broader questions – what are the major trading sessions, and when do they begin and end – there are no universally-accepted answers to those questions, because forex trading sessions do not start and end at fixed times (as trading sessions do in exchange-traded markets). Instead, in each forex market – the London market, for example – trading ramps up in the early morning, as the sluggish overnight period transistions to daytime, and then ramps down in the late afternoon, as the busy daytime period transistions to the overnight.
Most – but, not all – of the trading in any particular market occurs during the normal business hours in that market, say 8 am to 5 pm, local time. And those times are frequently cited as the so-called forex session times in that market. But, those times are merely a handy approximation.
The Babypips School teaches a 4-session trading day. The 4 sessions are Sydney, Tokyo, London, and New York. In this scheme, there are extensive overlaps between Sydney and Tokyo, and between London and New York. When basing pivot points on session times, you have to decide how to contend with these overlaps, as described above.
John Kicklighter, analyst at DailyFX, suggests a 3-session trading day, the 3 sessions being Tokyo, London, and New York. You can read about his approach in this article from Investopedia – The Forex Three-Session System | Investopedia
Keep asking questions. It’s how you learn.