The 'ring' device might only be able to connect to a 2.4ghz network. Since Eero is a mesh system, you might have to temporarily disable the 5ghz band or toggle legacy mode. I hope this suggestion helps the problem you are running into.
You can temporarily disable the 5GHz bands by tapping on Settings > Troubleshooting > 'My device won't connect', then tapping on the "Temporarily pause 5GHz" button. This will disable 5GHz for 10 minutes, which can help with setting up some 2.4GHz only devices.
