Should be done before new needles expand. If they are allready, better to wait until winter dormancy. If decandeled at the right time one more flush of growth can be expected in summer.
This is actually not true at all.
With all double flush pine, the only relevant variable is how long the growing season would be after you decandled.
The longer the season, the longer the needles and the internodes you'll get with the second flush.
Whether the first flush already opened entirely or not is entirely irrelevant, AFAIK.
As a consequence, you decandle smaller trees later, as you want smaller needles there, while larger trees get decandled earlier, as you want longer needles so they'll be in balance with the size of the tree.
So, coming to the OP, there's no precise time as to when you're supposed to decandle. Depends on the size of the tree and on how long your seasons are.
FWIW, here (northern Italy) I plan to decandle my chu-sized JRP in a week or two, whereas my mame/shohin JBP would wait at least until early july (except I'm not decandling it this year).
JRP's candles look like this, right now:
Of course your timing will very well vary.
Assuming your climate is more or less the same as in most of Europe (dunno where you're located), I'd suggest decandle in early june as a first attempt, and see the results. Next year adjust to later or earlier decandling depending on what you want to obtain.
Or even better, find experienced practitioners in your same area and ask what they're doing.
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I live in California. So the climate is Mediterranean. Right now, it’s practically summer. It’s hot with no rain. I’m not sure if my Japanese black pine would do well in my climate. Our winters don’t get too cold either.
Southern part I suppose? Weather in SF is usually pretty bad this time of the year (or at least it has been every time I’ve been there).
Anyway, this is where experience from local practitioners is invaluable. Plenty of bonsai clubs in California, I’m pretty sure you’d have no problem finding one close enough.
Doesn’t need to be an in-person thing: most likely they’ll have something like a forum as well...
Could even just be individuals with good experience and an online presence, these days; someone doing bonsai with good results and YouTubing about it. Grab knowledge where you find it