TEMPEST.114

I'm looking at it now, but just to warn you, if you upload a mission that has mods required - mention it in your post or remove them from a cut down version you share. 

As you're having a problem with just the recovery tanker then they shouldn't cause an issue; If I find something I'll post. 

ETA:

Okay, you've been confused by the nomenclature. 
1. You've added a 'Refuelling "REFUEL"' task - this tells the taker that it needs to refuel ITSELF from another tanker. As there isn't one, it's not doing anything.

Needless to say, that's a completely different task. Normally purely for fighters.
 
2. You're completely missing the instruction to tell it to BE a tanker.

 
3. You're also completely missing the instruction to tell it to BE a RECOVERY tanker - that's it's own dedicated task. It's here you specify the alt and speed AND the carrier it's supporting. This means it will continually follow and circle over the boat even as the boat moves about.

 
I've attached a demo mission that should show you how to set it up correctly.
It has the F14B in the client spot, but change that if you don't have the "best module in the sim". 😉
Recovery Tanker Working.miz

It seems at some point 'log' became it's own singleton; if you scrape all the .lua files in DCS World then they all do things like this:
  D:\DCS World\MissionEditor\modules\MeSettings.lua     Line   4: local log              = require('log') So I'm guessing this happened at some point after the unofficial documentation was made and it's out of date. 
I think I answered my own question. LOL

Yes the AI really is that dumb.
You have to plan for everything. Have a look at my post in the first page of this forum for the Mission Editor Manual.
 
You will find several SET OPTIONS that you can set on AI Units, that might help you, but other than those, then yes, you will have to create your own behaviour with a combination of triggers, trigger zones and waypoints, waypoint actions and triggered actions. 
E.G.

It's usually 127.5 but if it's been changed you're going to have to go into the mission and look. 

So, I have a workaround. I didn't have to rely on polling or the net singleton stuff... but my Superscript has a Player Manager script and through a little bit of cunning I was able to utilise that and the way that DCS works with / without events to make it work. 
I know it won't happen, but damn I wish MP had all the same events as SP... 

I've found if you get them to report something else, or even check in with your homebase, it shuts them up. 
But a proper way to do this must come from ED. So I wouldn't bank on it anytime soon. 

there are a few posts on here, but to a large extent it's a continuous grind that everyone is seemingly made to go through for themselves just because those who came before were made to. ED have zero interest in a proper, fully functional and documented API / Scripting engine.
i.e. when you want to know how to spawn a particular unit with a particular livery and loadout, you make a mission with nothing else but that unit configured how you want it in the ME. Then save the miz, extract the mission table and grab the group table and trim out the bits you don't need / mustn't use (again trial and error and a few hard to find helpful posts) and hours/days/weeks later you are able to spawn that unit.
When you've learnt how to do that to enough distinct units, you can refactor your code to do 'most' of it as a generic spawn method, but you will still have large branching if statements to cover all the corner cases.
ED haven't really bothered with a proper API, most of this is 'untested' or 'as is' and they don't seem to care about it one bit - going by the eons old wish lists that never gets done - let alone replied to - and the fact that they never seem to mention the ME or the API in any of their 'updates' or 'year ahead' stuff... 

There is no 'official' documentation - only what Grimes has done off his own back on the HOGGIT site of all places, but that's out of date a bit, misleading, missing stuff and sometimes very opaque.
This is what it is. It seems no amount of asking, begging, pleading or bargaining can get the devs or managers at ED to make it more usable or stable or fill in the many, many, MANY flaw/gaps/bugs/missing features that have been outstanding for 10 years or so.

You're going to have to treat this like a reverse engineering problem and with the help of kind people on the forums and searching for old posts, try and slowly piece it together. 
I say this as someone who started in ME mission design and lua scripting just about 6 months ago with no experience of lua or scripting and no understanding of the (awful) mission editor. 
It's been a very steep curve but there are some amazing and kind people on this forum (and a few that really, really aren't) and finally last month I was able to spawn the units I wanted at an airfield of my choosing at run time, and have full control of tankers and awacs and make them come to my players upon request and change their tanking alt and speed and even lead them to their chosen homebase whilst tanking. 
It is possible, but it's a long, long climb. 
And then be prepared for players to not give a crap about all your hard work.

FYI if you have ANY dialog inspector open on the right side of the Mission Editor the auto save won't save when its countdown completes, the countdown will just restart and wait until the countdown completes AND all those panels are closed.
Because the way the ME was written it doesn't understand these 'atomic' changes (another reason it doesn't have undo/redo) and at this point it's impossible to add in without a HUGE amount of refactoring (basically a complete re-write).
So yeah, this is known about and mentioned in the bug list, because people have lost hours / a day of work on a mission because they didn't understand or know this. 

What's the unit's ALARM STATE? Have you tried setting it to GREEN until it gets where you want it to go?