NJ state part year residency dates confusion

[njresident]

I lived in Washington state permanently till 31st July 2019. I then moved to New Jersey on 1st August 2019 for a full time permanent job located in New York. I stayed till 31st August in New Jersey with my wife (who had been living in New Jersey for years). Both of us then moved to a temporary accommodation in New York for September 2019 and then returned back to New Jersey in October 2019 to stay permanently here. Until October 2019, I maintained my household goods and USPS address in Washington. I am considering "married filling separate" status and confused if I should file my part year resident dates as August 2019 to December 2019 or should file it as October 2019 to December 2019?

[MaryK4]

You should file with August to December for New Jersey- you indicated that you were in New York at a temporary location but your moved in August for the job.