Don't see TM backup disk in migration assistant

Question

And it's in the finder - any suggestions?

Answer 1

Is it flashing (blinking) amber, or solid (continuous) amber?  If it's flashing amber, not solid amber, it may be working properly...
The flashing means Do Not Disconnect.  Solid color (whether red, orange, or green) means OK to Disconnect.
The color indicates battery charge status.  Red (very low) - Orange (not full) - Green (full or nearly full)
When flashing, it is never green, even if the battery is fully charged.
If the shuffle is set to Manually manage music (or Enable disk use), which means you drag songs to the shuffle in iTunes to load it, the shuffle's "disk" is continuously mounted when connected.  Therefore, the light always flashes ("Do Not Disconnect") because you need to eject the shuffle before physically disconnecting it.
If the shuffle is set to automatically sync, then the shuffle's disk is only mounted when syncing; at other times, iTunes keeps it unmounted.  Therefore, the light is solid (only flashes when syncing) and turns green when battery is fully charged, and you can disconnect the shuffle without the need to first eject it.
Immediately after a Restore, the default setting is automatic syncing.  The light turns solid green when battery is fully charged.  If you then set it to Manually manage music to load the shuffle with songs, the light will no longer turn green when battery is fully changed (it will continue to flash orange).