@user007 

Replying here to add to the only reference in the universe to this question :P

I dropped huge cash on the C4000 specifically for this purpose, so I'm really hoping it will work. 

To anyone saying it's not necessary to have an always-on Time Machine backup: Please go somewhere else with that opinion. Many of us have learned the huge value of hour by hour backups to rescue todays work that might otherwise have been lost. We bought these routers for this feature, so it needs to work well. 

TPLink claims to support Time Machine on expensive routers like the C4000, so they should also tell us how to get it done! Questions like what disk format to use are fundamental to making it work. 

Documenting below what I've done so far for the sake of others:

____________________

First try: Epic failure

• Took an existing Time Machine external drive that I had been using plugged in and plugged it into the router
• Went through the firmware steps (which were different from what's in the guide everyone links to 
• I thought I had set it up to "take over" the old backup, but once it started, it was clear it was doing a second backup to the same drive
• I decided to let it run rather than mess with it at that point
• Result: Crashed drive
• The drive stopped working with "missing drive" errors in Time Machine settings
• It showed as not available in the tplinkwifi web settings page
• Plugged it into my computer and got errors from macOS about how the disk was corrupt and could not be edited, but I could copy files from it before formatting it to make it work again. 

This reminds me of one of the cardinal rules of Time Machine: Never store anything other than a single Time Machine backup on a TM disk! Expect that all data on the disk will need to be removed and that having anything other than a single TM backup on it will eventually lead to failure. 

This always applies, but I figured I'd mention it because it CERTAINLY applies when messing with this half-hearted TPLink support for TM.

Second Try: Fresh drive with MacOS Extended (Journaled)

This is what I'm trying now. Some quick research indicated that MacOS Extended (Journaled) was the correct format for a TM drive, so I figured I would try it and see if the C4000 complained. So far the tplinkwifi.net interface seemed to find it fine, and let me select I: as the drive location in the Time Machine settings. 

As has become my practice when testing a problematic Time Machine backup, I'm starting with the Options > Exclude these items from backups setting in Time Machine set to exclude my entire user directory, so that the initial backup will be very small and complete quickly, before slowly adding more directories into it. This lets me test the overall setup without waiting days for my 700GB of files to transfer over. 

I'm now going to run the initial backup and see if it works! I wanted to post this first for the sake of others and myself when I inevitably Google for this problem in the future.  

UPDATE: So far so good

@jerclarke "the only reference in the universe to this question" Yup, it's really strange that this isn't a more common issue.

So for the record, my attempt has succeeded with an initial backup of about 60GB using MacOS Extended (Journaled) as the disk format. 

I'll have to see how well it lasts and how stable it is, but this is good news for me. Time to start working on the Excluded list and adding stuff back in until it's actually a full backup. 

@jerclarke I've been there. It eventually stopped working. I tried everything and eventually gave up. My backups are up to 700GB, took almost 24hrs each time and starting from scratch every week became  frustrating.  Without official documentation from TP-Link or Apple it's an exercise in futility.

I agree with you about the need for regular, hourly backups. I'm not sure why the rest of the world is ok with not doing that. TM wants to do it hourly. Having a MacBook, portable computer, means that backing up hourly to an attached USB is not practical.

@user007 Yeah. I have an ancient Time Capsule, which was slow as hell for backups but fairly reliable and Apple replaced it twice for free over the 8 or so years i've owned it. 

Needed a new thing for a new apartment and Time Capsule is a terrible value at this point, so am hoping SOMEBODY is making a working replacement for it. 

Here's hoping the C4000 has the extra power needed to not screw this up all the time. I'm preparing emotionally for the likely possibility that it turns out like yours did. 

@user007 

There is a solution and the best part is that you can use your disk interchangeably via USB and network at will!

To use Time Machine with any router without problems see here:

https://community.tp-link.com/en/home/forum/topic/205094?replyId=434304

@jerclarke I'd like to use my Archer C2300 for Time Machine and was wondering how your setup worked out in the end? Does it work reliably?

@NikoSilver 

When you first posted this solution, I asked if you have done a recovery. Do you know if anyone has so far done a complete recovery or even some file recoveries? Maybe at some point when I have an extra drive lying around I will try it and use it as a backup to my other TM backups. I do not leave my current TM backups connected all the time for security reasons.

@RayZ Absolutely not. It's trash. This feature should be removed from the boxes and manuals wherever it appears. 

It simply doesn't work reliably. I tried and re-tried, leaving my computer on for days and days while it did the initial backup, only to find it failing and unreliable!

Additionally, while it was "working" and even after it stopped "working" the drive was CONSTANTLY SPINNING. The sound that it would normally make when plugged into a laptop and performing an actual backup, but it did this NON-STOP. 

When I finally gave up, unpugged the drive, and tried to use it as a local backup target, it wouldn't work. I tried reformatting it in every way I could and nothing worked. 

Believe me: I wanted this to work, and I did everything I could to make it work (the evidence is in my previous posts) but it just doesn't want to. 

I dare someone at TP-Link to come here and tell us they have a long-term backup that works properly using this system. I've never seen anyone do so. I should have listened to the people on here who said it didn't work. 

I bought a big, expensive router specifically for this, I could have saved $100 and gotten a cheaper one that solves my problem. So frustrating. I'll pay almost anything to have this feature that I loved from my Apple Time Capsule but it seems it's simply not for sale, at least not from TP-LINK, at any price.