Paul Diamond you might benefit from "Working with extension tubes | Macro Photography | lynda.com"
https://www.youtube.com/watch?v=55IlBkVY4eY

In this video by Lynda.com the speaker recommends Kenko Extension Tubes and he speaks off their virtues and limitations (which are significant).

I have the Kenko Automatic Extension Tube Set DG for Nikon.
It does work as advertised...

That said here are important caveats I've discovered in using them.
1. Always attach to the camera body first (otherwise the electronics may not work as designed)
2. Consider limiting your optic to a lightweight 50mm (or similar). These tubes are not robust.
3. Only use a single tube at a time... Experience is a brutal teacher.

Other very important issues:
1. Depth of field is a huge problem! You will want to stop down to f/11 or f/16
2. Likewise these are an epic failure for available light.. f/16 combined with high magnification limits acuity unless you are locked down on a solid tripod, even then you subject will likely move.
3. Please realize that you will likely need off camera flash for publication quality imagery...

Now the good news...
any cheap manual flash will do...
However you will be far better served with a Nikon compatible Speedlight attached to a SC-29 $80 (or 28 $50) cable. This will allow for full iTTL control (which can be fine tuned with Flash Compensation.)

There... I've just given you months worth of R&D trust you'll be able to put this to good use...

FYI: If you are serious about macro photography you will ultimately obtain a macro lens...
I have the AF 200mm f/4 ED IF micro Nikkor which is considered an industry standard... Trust me it is...
That said I also have the Tokina AF 100mm f/2.8 which is a virtual gem... use it for both macro and more so for beauty genre... save your money and pick up the Tokina at less than half the cost of the similar Nikkor.

All the best on your journey Paul Diamond
Please stay safe and wear a mask while in public...

The Kenko tubes are a good value and I highly recommend them. For $129 you get three tubes: 12mm, 20mm and 36mm. You can use them individually or combine any two or all three for greater extension. They maintain full lens functionality and are well made with strong mechanical lens latches (which can be important!).

I don't know if the current Kenko tubes are metal. The older ones I've used for around 15 years (with my Canon kit) certainly are.

If the lenses you plan to use with them are relatively lightweight, the $79 Vello/Opteka extension tube set (same sizes as above) is an alternative. They are plastic and lighter built than the Kenko... but would probably be fine so long as you aren't using them with particularly heavy lenses.

Avoid the really cheap sets (under $25). They don't have any electronic contacts to support AF, VR or aperture control on G series lenses. You might be fine with manual focusing close-ups... And losing VR isn't a big deal, particularly if using a tripod... However, not having means of controlling the aperture of modern lenses is a problem. This type of extension tube is okay for use with vintage lenses that have a built-in, mechanical aperture control ring.

It's the same problem with Nikon's own PK-11, PK-12 and PK-13 extension tubes (sold separately for $90 or $100 apiece!). There is no means of aperture control with many modern lenses. They also don't support AF or VR, but, again, those are things you can live without. The lack of aperture control with any G-type lens is a problem, though.

EDIT: Image quality with cheap sets of "close-up filters" really sucks. There are better quality, such as the Canon 500D and 250D (both in very limited sizes). HOWEVER, even those cost some image quality. I've used them, still have one (77mm 500D), but prefer to use macro extension tubes with no optics to spoil a lens' native image quality capabilities. The better quality diopter lenses ain't cheap, either. For good ones, you'll pay as much or more for one than for a set of quality extension tubes... and the diopter lenses will be more limited in their usefulness, only usable on select lens diameters. Macro extension tubes, on the other hand, are highly universal... can be used with practically any lens.

I also just came across a Movo 25mm extension tube selling for $35. I have no personal experience with it, but according to the description it's all metal (aluminum). Whether it's up to the quality of the Kenko or not, I don't know. https://www.bhphotovideo.com/c/product/1542435-REG/movo_photo_ext_n25_25mm_af_extension_tube.html

Don't you mean the 600mm FL f/4? I wasn't aware of a 600mm PF, only a 500mm PF, which is an f/5.6.

BTW, The 500mm FL with a TC-14E III 1.4 extender gets you 1/2 that distance closer @ ~750mm. & is lighter & Hand hold-able thsn the 600mm FL. I do it all the time with my D850 for dragonflies to birds.
Using any other than an altered Nikon converter is risking a catastrophe. I had a Kinko break and drop my 105mm lens. It was ok, but I would never put one on either a 500 or a 600 FL.
Time to downsize?

Nikkor 600mm F/4G AF-S VR Lens Just bought, not yet arrived. Closest focus is 14 feet. My Nikon 200-500 zoom focuses to 7.3 feet and does great out to about 15 feet with what we would consider 'macro' subjects. It's a bit like always longing for a longer reach telephoto lens than the biggest one you own. Because I own a 200-500 f5.6 zoom, I wanted a PF that would be at least a bit better/longer. And I thought about size/weight of the PF lens on a heavy camera body. The D850/200-500 is about 8 pounds. The D850/600 PF should be about 3 pounds heavier. Hopefully bearable as a weight from the custom 600PF neckstrap or with a Manfrotto monopod attached as carry weight. We will see.

I'm seeking advice and help, please. I shoot with Nikon D800E and D850, a variety of lenses. I need to buy an extension tube or set that will give me closer focus without losing auto exposure or autofocus features of my lenses/cameras. I haven't found any yet. I'm hoping fellow Hoggers can help point me toward something that will work for me. If you have personal experience using the thing you are recommending, even more valuable advice.

Thanks for reading, and for your help, please.

Promoter also makes a set of ext. tubes which maintains communication between body and lens (cat#8819) and sells for $110. Find those at a Promaster dealer camera shop. Marumi makes some nice Achromat multicoated two element close-up filters if you wish to check out that route. One thing to keep in mind is that depending on the amount of light, max. aperture of the lens, and amount of ext. tube extension, bellows factor could effect the amount of light getting to the AF sensors, thus possible trouble autofocusing. Reverse rings can be a lot of fun, tho somewhat limiting and no AF.