Suppose I have two routers configured in master/slave configuration.

They look something like this (addresses are not real ones)

123.123.123.10  <===> [eth0] Router 1 (10.1.1.2) [eth1] ===> +----------+
                                                             | 10.1.1.1 | ===> LAN
172.123.123.10  <===> [eth0] Router 2 (10.1.1.3) [eth1] ===> +----------+

The 10.1.1.1 is the default route for the Network (10.1.1.0). What's slightly different in this config to other's I've seen is that I don't have an external virtual IP. Also, the 10.1.1.1 addresses are in real life, public IP's (not private ones shown here). This is more of a router setup than a firewall setup so I'm not using NAT here.

Now the issue that I'm having is that I can't see any way to configure UCARP or VRRP to monitor both eth0 & eth1 and fail over to the backup router should either of them go down. What I'm seeing is that if Router1 is the master and I unplug eth0 on router1, it doesn't fail over to router 2. However, it will if instead I unplug eth1 of router 1.
In VRRP I see there is a cluster group, but it seems that for this to work you need to have virtual ip's or vrrp instances rather than actual interfaces assigned to it.

I hope my explanation is clear. How do I get around this?