How do I connect my router to my Time Machine backup?
Here is a question and an answer. I bought a new Linksys router and to my horror discovered it does not handle time machine tasks well. The device reads HFS+ well, but wasn't seeing my drives correctly for sharing media. For some reason, It did not want to share my media files but rather my backup directories. I attached my old airport extreme - N to the Linksys using a CAT5e cable. I reserved an ip for the Airport and created a static address. Use the Linksys as your default gateway and DNS. Turn off DHCP and WIFI from the AirPort. I used account passwords for a drive I had partitioned into 3 parts for each time machine backup.
You should be able to see your airport in it's utility via your new wifi. Share the disks. Open disk utility and create a new disk image as a sparsebundle. there are instructions all over how to do this. Connect to the drives by selecting go-> connect to server and type the ipaddress of your airport extreme. You should see the drives Place the bundles in each partition and your time machine aps should see the new drives.
The old airport extreme is just a backup drive and the new router is a faster media server.
Hope this helps someone.
MacBook Pro with Retina display, macOS High Sierra (10.13)