It is usually 12 days for gold and 18 for Platinum.
Also when I called and did mine a few years ago the CSR told me to call about the 2nd or 3rd of the month that way you get that month plus 3 additional months to earn it. It was true for me, my sis and mom.
Just on a side note, if you are close you can book a meeting room for 10 elite nights. My mom was short last year by 8 nights. We booked a meeting space for my daughters bday party. cost was about $150, they let us have access to the pool and the 9 years old thought it was great! (And I didn't have to have them at my house)