Thank you for your response. It turns out the accessibility on my modem is absolutely dependant on the internet connection (as the orginal poster claimed).
The 192.168.100.1 page loads and works fine with the cable disconnected. It continues to work after the cable is connected until the last light on the modem goes solid. I have tested this several times.
It seems cox blames arris and arris blames cox. I have been in contact with Arris multiple times. Near as I can tell I am guessing both are right. I would wager that Arris had/has a software load with this issue and cox is using it as there approved version. Or perhaps my version hasn't updated yet.
My version is (in case it helps, looks to be from 2022): AC01.01.008_122722_8200.03.07.733.CT