No idea why it won't show..
Try clearing out all the current wireless connections.. and start with nothing connected but the wifi turned on.
Do a factory reset of the TC and see if it shows up.. you should work on it in the same room as the TC.
If it fails again make sure you have ipv6 local link turned on for the wireless connection.
This is necessary for the utility to work.
No luck then buy the USB or Thunderbolt to ethernet dongle. Apple sell the later for just $10 more and it is well worth the expense.. IMHO you cannot operate in the modern world on wifi alone. It is just not that reliable or fast yet.
Use another computer.. a windows PC even or ask a friend with a laptop or an ipad.. iOS version of the utility seems to have less issues than the Mac OS one.