The current working theory is that it takes 4 seconds from your last knife/melee attack to recharge - in other words, if you are knifing constantly (working toward a melee challenge etc.) you will not see it activate every 4 seconds because you are not waiting 4 seconds in between.
This is one possibility. The other possibility is that the upgrade sucks. Considering how Stun Armor "works" there is a high likelihood of this scenario.
I find the electric knife upgrade quite useful. For starters once you acquire it, sometimes when you get hit the electricity will arc due to being in combination with stun armor, I've witnessed this on many occasions. As stated before it will only work while knifing every 4 seconds of not using your knife. Later on in the match, if in a pinch I've knifed a cryptid for the arc effect to stun nearby foes. It only costs 30 teeth, thats literally 2 games. Definitely worth it imo.
I find it has it's uses. Especially during those percentage challenges in combination with stun armor, and flaming riot shield. It can help out a lot.
Or you can just throw out the Vulture for $2200 and save those teeth for something else.
But I still like it.
If you hold your reload button and melee, you shouldn't have to wait for 4 seconds to recharge (square for PlayStation and X for Xbox). Here is the video.
COD Ghosts DLC Nemesis - Infinite "Electric Knife" "Glitch" (COD Extinction Exodus DLC) - YouTube