Your routes and configuration look fine.
$: route -n
Destination // Gateway // Genmask // Flags // Metric // Ref // Use // Iface
66.*.*.0 0.0.0.0 255.255.255.248 U 1003 0 0 0 em2
0.0.0.0 66.*.*.1 0.0.0.0 UG 0 0 0 0 em2
The first route, 66.*.*.0/29 with gateway 0.0.0.0 tells your computer to use interface em2 and then make an arp request to find the hardware address of the host you're trying to reach. This is a "connected" route.
The second one is the default route, pointing at your default gateway through em2. If you need to send a packet in another network than 66.*.*.0/29, your computer will make an arp request to find 66.*.*.1 and then send the packets to it.
The only thing in your configuration that could be an issue is the NM_CONTROLLED=yes statement in /etc/sysconfig/network-scripts/ifcfg-em2. This tells the system that this interface is controlled by NetworkManager. This could interfere with your static configuration.
However, even without any default gateway you should be able to ping and ssh from the 66.*.*.0/29 subnet to your machine.
Check layer 1 first, and ensure that the cable is plugged on each side. Use leds on nic and switch, and check if the system sees it correctly:
# mii-tool
eth0: negotiated 1000baseT-FD flow-control, link ok
Then verify if any iptables are dropping the packets. Use iptables -L or iptables-save to check for any rules, and iptables -D <rule> to delete them. Pay attention to the default policy.
Also, on some systems, NetworkManager can configure ufw automatically, and I've had issues with static interface configuration that wasn't seen by NM and hence blocked by ufw.
For any network device which is not my default gateway, I usually set the default route flag to no:
DEFROUTE="no"
This seems to work without any issues for my servers with multiple network interfaces. If you then restart your network service or interfaces, you should be able to check the routes to see that this is actually working:
/sbin/route -n
Hopefully this helps.
Best Answer
Sure, nothing stopping you from doing that. The network interfaces will see broadcasts for the other both subnets, but that probably won't make a big difference unless you have a really busy network.
You cannot have 2 default gateways. Remove a gateway from one of those interfaces. Having 2 like that simply isn't going to do anything useful. Only one of the gateways will be used.
DNS resolution (resolv.conf) really has nothing to do with your routing configuration. On Linux DNS resolution is system wide and really has nothing to do with the interface configuration at all. Just place a couple valid DNS servers in your resolv.conf. If you need something more advanced to send some requests to different upstream servers you may need to install something like DNSMasq.