You need to leave GIE OFF, since there's no Handler for it to jump to.
But I think you're right, you may have to turn TMR1IE on to get it to Wake-Up.
TMR1H.7=1 will work too. But it's waking up twice as often as needed, and will use twice the power.
And after a month, a 1 second difference is less than the error rate, so attempting to get 1 second accuracy is futile at best.
DT
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