I purchased two out-of-state rental properties in Nevada. One as a second home (11/2020) and one as a rental/investment property (12/2020).
the first property would be a second home since it was not rented until 2021. (not really sure by what you mean by rental property/second home). a rental that is used as a second home can be limited in what can be deducted based on days of personal usage. so for 2020, you would be entitled to home mortgage interest deduction and real estate tax deduction on schedule A. this would require. since it was not rented you may need to enter the cost and other info for rental on schedule E in 2021. the rental property also would not be entered until 2021 when it was rented.
see this link regarding personal use of rental property
https://www.irs.gov/taxtopics/tc415
