The Ethernet jack on the STB's is not activated. It does nothing.
There are lots of threads on this forum discussing the various ways to add another router. In short, you can connect to the Ethernet port on the primary router or use coax. Spend a little time searching this forum and you'll find good advice. The FAQs at broadbandreports.com are very good, too.
can I add a second router via a set top box or do i need to connect it to the coaxial jack from the wall?
You can add a 2nd moca (coax) connected router to any coax connector that is on the same coax network as your Verizon router. First configure the 2nd router by turning off the dhcp service and giving it a static address on the same subnet as the Verizon router 192.168.1 then connect it to a coax port, if you have a tv connected to the coax port you will also need a splitter.
You can add a 2nd ethernet router anywhere where you have an ethernet jack that is connected somehow to a lan port on your Verizon router.
If you're going to bridge it to the Verizon router then first configure it the same way as the moca router above and connect it to a lan port on the 2nd router.
If you are going to double nat the second router then first configure it to be a different subnet to 192.168.1 e.g 192.168.2 by setting the dhcp settings to that new subnet address. To make life easier for yourself you should set the wan address of the 2nd router to be a static address on the 192.168.1 subnet. Then connect the ethernet connection from the Verizon router to the wan port of the 2nd router.