Myself, I think it is 100% random if he appears or not but I have heard theories of situations that might improve the spawn chance of him in a delve,
Everything from a higher chance in Axj-Kahet delves to the same in delves with candles.
Also killing all the empowered mobs by him would also raise the chance for him to appear.
Is there any truth to this or is it, as I have guessed, totally random?
Random . it’s 3~5% per dungeon to spawn .
Sometimes you may be lucky sometimes (40~50 delves completes without seeing once )
As i Guessed then…
Yeah no, Zekvir is definitely not a 5% spawn chance.
I’ve done more than a hundred delves and I would say he has atleast 15% spawn chance, if that’s even how it’s measured.
If you rub your belly clockwise and pat your head while fighting an empowered mob it increases the chance he’ll spawn.
Honest.
Really?
I have to try that. 
But magicians have calculated that million-to-one chances crop up nine times out of ten.”
I’m not sure but I have seen him pretty frequently. I was speed-levelling this new alt that I’m posting on and he came at me in the first room of a tier 1 last night. One of the few times I’d rather he had not spawned.
I was Delve running with a friend a few days ago and Zekvir was kind enough to show up in every delve we did that night 
First time this had ever happened for us, so I would say it’s definitely random.