Finding the IP address of a walled in router

Why are you so sure your dd-wrt switch has an IP address? If you look up the DD-WRT wiki, it says that you can achieve a simple AP as follows:

Simple Version

Disable DHCP

Connect a LAN port to the main network / to the main Router's LAN port

Now you have an AccessPoint only setup, where clients are served IP details from your main network or main Router.

The WAN port is not connected, so it is not given an IP address. Switch functionality of course still works.

Let me expand on this. DD-WRT, like OpenWRT or OpenWRTUSB, uses hostapd for setting up the AP. Since you have a remote DHCP server, the hostapd interface will have to be bridged with an ethernet interface, so that all DHCP-related traffic can be properly forwarded to the DHCP server: the alternative (a NAT configuration) assumes that the wifi clients are inserted in a different subnet, with addresses dished out locally.

It is however a common misconception that bridges need an IP address to work: bridges are Layer-2 objects, not Layer-3. Having a bridge without an IP address means only that the device to which the ethernet and wifi interfaces belong cannot be reached from the network, that's all.

The fact that bridges do not require an IP address to function properly is discussed in many places, I will just point you to the one where I first read it. Here it is stated that:

It is worth mentioning at this point that it is perfectly possible for the bridge to be able to operate without having an IP address assigned to it. If this were the case, it would bridge packets between the two segments as shown above, but would not actually take part in any network exchanges on an IP level.

Stated otherwise: the fact that you can connect to the SSID by no means implies that the SSID has any IP address of its own.

Perhaps this is the reason why even a deep nma scan was unable to identify the address in question.

EDIT:

And yes, btw, I did test it on my Debian system. I do not expect it to be any different on DD-WRT.