So you have used interrupts and know to make variables used in interrupts as volatile?
And you know that time is kept in unsigned long variables?
How long can you aim at dark sky to get measurements? 3 seconds? 30 s? 300 s? 30 minutes?
Maybe the best way will be to count pulses and see how long that takes.
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You understand, if I stop when pulse count is done I can know how many whole usecs (microseconds) it takes but I can't know the fraction of a usec after the last full usec. If it was 400001.7 usecs, I will miss the .7. That is an unavoidable (and small) source of error.
If I stop on a time count while also counting pulses then I can know the usecs and how many pulses but not the fraction. If 100 seconds takes 50.8 pulses, my 100 second read only sees 50.
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Since pulses are so big compared to usecs there will be more possible error counting over a set time than counting a set number of pulses and seeing how long that took. I would rather have a fraction of a usec (really, Arduino is good to 4 usecs which is still very small) as error than a fraction of a much bigger pulse as error.
What decides the method for me is the way with the smaller error. In this case, it's pretty clear?
So big open to the forum just to be sure question --- can you read micros() in an interrupt?