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The reality is as you said is it's different for every underwriter and mortgage lender. It could be the first thing they do or the last. Also they might check multiple times. During the final two weeks before I closed, they checked my employment 3 times. They were still doing other things also. I know it's stressful to wait but the best thing you can do is ask for regular updates and just let them do their processing.
Good Luck on your new home!