i think that this is referring to her husband's infidelity. i think she wants him to come clean and set her free as a 'gift' to her. i think with every lie, every clue to his infidelity, he is dragging on the torture.
Let it not come by the mail, finger by finger.
Let it not come by word of mouth, I should be sixty
By the time the whole of it was delivered, and to numb to use it.
she just wants to be free but she is not willing to be the one to give up. she wants him to give her the ammunition so she can pull the trigger.
THe 'Birthday present' could b the omnipresent veil of time that constantly closes in on her, and she begs it to kill her directly, not 'finger by finger', that might take 60 odd years. What do u think?