Not 100% sure about rental income, but I know in my business I claim income when it is made (I also use the cash basis for reporting).  I do believe that you are supposed to report the income when it was received in your hands.

Agree that the income needs to be reported in 2019. The problem that I have is working through the expense deductions for rentals, ie taxes, HOA fees, property manager costs etc.  The IRS method apparently accounts for personal vs rental use in determining how to allocate these.  The problem is that the income was received in 2019, but the rental use is in 2020.  It is not clear whether I will have another renter in 2020 to declare rental income for 2020 going forward.

You report rental income in the year you received the income.  The income you received in 2019 will be reported on your 2019 tax return NOT your 2020 tax return.

Rental income/calculations that apply or occur in 2020 will be reported on your 2020 tax return.