Linux – Don’t get ICMP reply when ping from specific interface

I have a linux machine running under CentOS with 2 ISP. My rollover ISP channel script try to determine when we at secondary ISP channel is there a primary ISP channel get up and vice versa when need to change from primary to secondary. Normal thing.

To do this i want to ping from interface which now is not default gateway.

My 2 ifaces is eth1 is primary and eth2 secondary.

When we at eth1 for example and want to check is there internet on eth2. Eth2 is in up state.

ping -I eth2 8.8.8.8
PING 8.8.8.8 (8.8.8.8) from 1.2.3.4 eth2: 56(84) bytes of data.
^C
--- 8.8.8.8 ping statistics ---
15 packets transmitted, 0 received, 100% packet loss, time 14173ms

But my running tcpdump shows that packets are sent and delivered to server, but some reasons don't seen by ping utility. Why is that i have no idea? What may be cause?

tcpdump:

17:36:42.191153 IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto ICMP (1), length 84)
    1.2.3.4 > 8.8.8.8: ICMP echo request, id 44138, seq 1, length 64
17:36:42.235899 IP (tos 0x0, ttl 59, id 30465, offset 0, flags [none], proto ICMP (1), length 84)
    8.8.8.8 > 1.2.3.4: ICMP echo reply, id 44138, seq 1, length 64
17:36:43.190616 IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto ICMP (1), length 84)
    1.2.3.4 > 8.8.8.8: ICMP echo request, id 44138, seq 2, length 64
17:36:43.235363 IP (tos 0x0, ttl 59, id 31136, offset 0, flags [none], proto ICMP (1), length 84)
    8.8.8.8 > 1.2.3.4: ICMP echo reply, id 44138, seq 2, length 64
17:36:44.190575 IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto ICMP (1), length 84)
    1.2.3.4 > 8.8.8.8: ICMP echo request, id 44138, seq 3, length 64
17:36:44.235346 IP (tos 0x0, ttl 59, id 32083, offset 0, flags [none], proto ICMP (1), length 84)
    8.8.8.8 > 1.2.3.4: ICMP echo reply, id 44138, seq 3, length 64
17:36:45.190554 IP (tos 0x0, ttl 64, id 0, offset 0, flags [DF], proto ICMP (1), length 84)
    1.2.3.4 > 8.8.8.8: ICMP echo request, id 44138, seq 4, length 64
17:36:45.235368 IP (tos 0x0, ttl 59, id 32355, offset 0, flags [none], proto ICMP (1), length 84)
    8.8.8.8 > 1.2.3.4: ICMP echo reply, id 44138, seq 4, length 64

netstat -rn shows that eth2 not default gateway sure, but it eth1.