DS3231 RTC
As the Rigacci blog mentioned, the RTC we purchased did had a recharging circuit and the battery we used was a CR2032 which is non-rechargeable. The surface-mount resistor was removed as shown in the diagram (200 ohm resistor).
Continue on with rest of the hardware test as stated in the blog.
Here is how your setup should look like with the RTC connected, note only 5V/VCC, GND, SCL, and SDA need to be connected. The 32K and SQW should be left not connected.
The documentation in the Rigacci blog was sufficient to properly install the RTC, although i skipped the AirPi software portion for now as i wanted to focus on getting the RTC working first.