H1B - Between jobs days - 60 days grace period

My H1B petition got approved with new employer and I am going to resign my job with present employer, my question is,

Are the days between jobs counted with old employer H1B petition’s 60 days grace period or new employer’s H1B petition?

PS: I believe Old H1B petition has a 60 days grace period and the new employer H1B petition also has a separate 60 days grace period, please correct me if my understanding is wrong

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