buy rental with cash and then cash out from another rental?

I have been searching and reading many posts but still confused.

My situation is:

1. Bought rental house A with cash, used up almost all my cash.

2. Immediately did cash out refinance with my other rental (B). B is almost paid off so I pay tax on rental income. The cash from refi is now in bank.

These two events happen quickly (<90day)

I want to know if the interest I pay on B can be FULLY tax deducted from rental income (assume income > interest)?

I always assumes that's the case, however just came to realize this could be a problem.

I know for primary house sequence of 1 and 2 are not important (https://www.irs.gov/pub/irs-pdf/p936.pdf:

You buy your home within 90 days before or after the date you take out the mort- gage.) But I am not sure about rental.

If I can't fully deduct, what is my option, can I pay back B's mortgage to match the loan amount it was? Or I have to buy another investment property with this money? B is quite new so there's no improvement I want to do.