You shouldn't need the USB cable plugged in for it to pair.
The ring Gen 2 devices can be very picky. Did you pair it with S2 security or change any of the security parameters. They need to have exactly what they ask for when they prompt you for security through either the app or through Smartstart. Without that they just will have problems.
I had a few issues getting my to pair fully as well. I finally had to hold the little reset button on the back to get it to rully reset and then add it with Smartstart.
Check Live logging to see if anything is logged when pressing the buttons and such. If not it probably didn't fully pair and needs to have everything reset.
