|The IP will only appear in the arp table if you've pinged it or possibly done a trace route to it as far as I know.|
But if I assigned a strange IP then I guess I can see why that happened.
Yep, if you typo'd and entered 192.168.0.12 or 23 or something else, then you won't be able to access the router using 192.168.0.2
It has been set up in this faulty config for about 2 weeks. I wonder if that's relevant?
It will be relevant, yes.
Leave it setup as it is now. Reboot the router. If you can't access it, or ping it at 192.168.0.2 then move the network cable from the WAN port and put it in a LAN port and try pinging/accessing it again. If it works then it was just a simple matter of the cable being in the wrong port.
Last night when troubleshooting I realized Ethernet from router 1 was coming into the WAN port on router 2. I was probably seeing router 2 in the DHCP client list at that point.
Yep, makes sense. The WAN port will likely be set to DHCP and got a valid IP from the DHCP server in router 1 and that's why everything connected to router 2 is working.
I suspect just moving the plug to router 2 will fix the issue and it will be accessible at 192.168.0.2
I use my method (LAN port to LAN port - with static IP on LAN side of downstream router) so I always know what my IP is in case I need to access the router's management page. If I used the WAN port and DHCP, I probably wouldn't and then would run into the same issue as you're having. I use static IP assignments on a lot of stuff, printers, servers etc.
Let me know if you get it working!
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.