Those second ports on some modems don't have a standardized function, so, yeah, we'd need your make/model if you want to tinker with it.
For example, some second ports are Switched ports akin to the ports on your router. This means you could connect a device to the port and it'd be on your personal network; however, that device would not have Internet access. It'd be good for a locally shared resource.
You could connect your security system to the port; however, being on the Cox network, the port may be locked to only Cox' security system.
It could also be an inactive WAN port (Internet access). Cox normally only assigns one public IP address per account; however, if you needed another public address, Cox might be able to activate it. It depends on your make/model.
I have gigablast and for the money I pay for high speed internet, I'd like to be able to use both ports for my wired devices with Ethernet switch. how do I go about setting up another IP to use this port?