log will show you the relationship between the device name, irq, address, and MAC, for example:
dmesg | grep 'eth.*irq'
I'm guessing the mapping address at least will be consistent (and different) between the two interfaces, but I don't know what your ethernet hardware is.
You can also use lsdev
in combination with ifconfig -a
I take it the MAC addresses aren't labelled on the appliance (I'm assuming you will edit /etc/udev/rules.d/70-persistent-net.rules
to force the device name based on MAC address).