Rental income (documented) vs. rental history

[Benjamin Christian]

Later this year I plan on purchasing my second rental property (first was my prior primary residence and now is a rental).  My first rental does not show on my tax returns the last two years, but the rental history is perfect so far.  When I apply for a loan to purchase another rental, will my rental history (shown with past and current leases combined with bank statements proving rental income) be enough, or will I absolutely have to show it on my tax returns?  I am trying to decide what to do soon, before I file my taxes for 2020.  Thanks!