So, long story short, I realized I could teleport to the Argent Tournament on my Dark Iron, so I did so…
…and I showed up missing on my screen. I asked around and no one else could see me either.
Examples of what I mean, this is me using Drain Soul to show where I am:
https://cdn.discordapp.com/attachments/530130800289775625/777434672874651648/WoWScrnShot_111420_232550.jpg
And this is me high in the air on a flying mount:
https://cdn.discordapp.com/attachments/530130800289775625/777434645721645066/WoWScrnShot_111420_232617.jpg
I will try logging and reusing the mole machine tomorrow, and update the post if it’s an easy to replicate thing, or just a rare occurrence. (Based on whispers I got, it’s happened to other people over the past week)
EDIT: Completely replicatable. Teleport to Argent Tournament grounds and you’re invisible until you log out. Death will not fix it.
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This happens to me too every single time I use the Mole Machine to the AT Grounds.
Only fix is to log out then log back in. Then the character is visible again.
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It almost sounds like a reverse phasing effect: you are kinda transported to the old (pre-event) tournament grounds but the world around you is phased to the Shadowlands event. I say “kinda” because you can still interact with the SL phase.
Blizzard bugs are so creative and interesting. At least the log-off/log-on workaround seems to be available.
This is happening to me as well. A guildie suggested that I should be queuing for battlegrounds, and is imagining an untargetable flag floating around Warsong Gulch. I might actually even enjoy pvp if I could do that. 
They can target your nameplate still, even while invisible.
But for people like me who play without nameplates on, yes you’d be untargetable, but you’d also likely get a ban for exploiting.