When I was born my mother worked as a nurse.
When I was born my mother was working as a nurse.
Is there any other difference than the job being permanent/temporary? Is this an example of an interrupted event?
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I think either sentence could be used, regardless of whether the job was permanent or temporary. The meaning of the sentence is the same: Your mother was employed as a nurse at the time you were born. She may have continued that career after you were born, or she may have hung up her stethoscope to take care of you. You can’t infer one or the other based on the used of worked or was working.
The sentence becomes more vague, though, if you change it slightly:
When my cousin was born, my mother was working as a nurse.
In this case, it’s not clear if you mean that your mother was pursuing a nursing career during the year your cousin was born, or if your mother was a nurse in the delivery room at the time and on the day your cousin was born. It could mean either one of those.
That ambiguity isn’t in the original, though, because, presumably, the woman giving birth doesn’t work as a nurse during childbirth.