Linux does not directly track the uptime of a particular interface, so you could try searching the various /var/log/messages* files trying to see when that interface was first brought up (and when it may have gone through a transition which will also increment the "carrier" counter shown by ifconfig -a). But for the external interface in particular you could look at the age in seconds of the default route leading out that interface like this, because if the external interface goes down the route will be removed and have its age counter reset:

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