Have you tried something like tcptraceroute from the client machine? That will reveal the network path without falling foul of firewalls that are blocking icmp.
Or are you saying you don't know which interface you need to have SSH listening on? If that's what you mean then you can infer the answer from your routing table, so for example if your client machine is
192.168.1.1 and your server is multi homed with interfaces
eth0 172.16.1.2 and
$ ip route get 192.168.1.2
192.168.1.2 via 172.16.1.1 dev eth0 src 172.16.1.2
Would tell you that ssh needs to listen on eth0