Use ping com a tecla -I e IPv4:
ping -I eth0 -c 1 ROUTER_IPv4
ping -I eth1 -c 1 ROUTER_IPv4
Exemplo:
hostname ~ # ping -I eth0 -c 1 192.168.1.1
PING 192.168.1.1 (192.168.1.1) from 192.168.1.3 eth0: 56(84) bytes of data.
64 bytes from 192.168.1.1: icmp_seq=1 ttl=64 time=0.314 ms
--- 192.168.1.1 ping statistics ---
1 packets transmitted, 1 received, 0% packet loss, time 0ms
rtt min/avg/max/mdev = 0.314/0.314/0.314/0.000 ms
hostname ~ # echo $?
0
hostname ~ # ping -I eth1 -c 1 192.168.1.1
PING 192.168.1.1 (192.168.1.1) from 192.168.1.3 eth0: 56(84) bytes of data.
From 192.168.1.3: icmp_seq=1 Destination Host Unreachable
--- 192.168.1.1 ping statistics ---
1 packets transmitted, 0 received, +1 errors, 100% packet loss, time 0ms
hostname ~ # echo $?
1
hostname ~ #