Little Snitch’s outbound firewall tells me that automountd wants to connect to Backups.backupdb on port 111.
We found out that this is caused by our switch to the free OpenDNS service.
It is Time Machine trying to mount a remote NFS (network file system), but cannot.
We told Little Snitch to Deny, but you can also log into your OpenDNS account and they offer a way to exclude certain non-existent domains from being subject to the “search results” page response of hit-nxdomain.opendns.com. You can add the domain name of “Backups.backupdb” to the “Typo Exceptions” list and OpenDNS will return a straight NXDOMAIN response when queried for that domain.