Is employment checked again at closing (FHA loan)?

I'm in the process of finding a home to buy (FHA loan).
I'm not worried about my credit being checked, my score is 822 and has been 800+ my whole life.

However, my employment may change soon. I currently work part-time and want to take a full time position that pays me more. My wife works full time. I've heard that I shouldn't change anything in regards to income during the process, but this is a change for the best. Even if I was to lose a new job I have enough saved to pay for 3 years of mortgage payments, plus what my wife makes.

Would they even know that I changed jobs? They have already verified my employment and seen my pay stubs for per-approval, would they do it again at closing?

I have read most people say that I need to let them know, but if I don't have to I would rather not have to go through all the paperwork trouble again, especially when I'm not worried about being able to make payments.

I've looked everywhere for a straight answer on this but have yet to find one.

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