i just pulled a choke assembly apart. that hole/passage doesn't connect to the vacuum port of the carb or the suction side of the choke piston. i believe it to be a relief port (probably backfire relief) for the body of the choke assembly. if the assembly is carefully looked at you'll even see a small screen in the relief passage. it's supposed to be the way it is. i also think the passage could be considered a type of vent,

Here's one I pulled off an Eddy. OP, I don't need this- PM me if you want it. It has no hole. And that passage is connected to the inside of the choke housing.
Edit- couple of pics of AFBs with heat tube fittings in that spot. Cold air to cool the electric coil? I'd prefer no vacuum leak.

I figured if the picture was right side up the car must be upside down.

i always thought upside down was correct on moparts?

doing more thinking,and knowing the hole/passage is a vent to the atmosphere, this thing could also relieve some temps from a constant 12v heat source. the screen definitely keeps stuff from getting in but will let stuff out. how many times have you seen the black plastic covers melted and drooping?

DO NOT PLUG THAT HOLE.

You have the vacuum actuated piston inside that has vacuum on one side and that that hole is the vent on the other side.

Whomever says plug it doesn't know what they are doing.

Actually I do know, at least enough to ditch the junk Eddy and get a Holley.
Edelbrock added that "cooling" port rather than make the choke cap out of bakelite as the early caps were made of. See above pic of early Eddy choke housing- no hole.

If the picture had been right side up,a lot of confusion could have been eliminated by seeing the hole is in the bottom of choke housing and not the carb.That's what happpens when everyone uses their i phone for posting pictures!

The only "vent" for the choke module is the opening in the bottom of the choke housing below the plastic cover (usually threaded).

You are just saying what they did with the older carbs before they had electric chokes basically and I can see it makes sense. The choke piston in the housing does not had a perfect seal or rings or an o-ring on it as vacum leaks past the piston and on the older carbs the vacum source was a slot in the choke piston housing that only pulled the piston as far as it could until end of the vacum slot gets uncovered by the piston as thats as far as the piston pulls and then you can bend the linkage to adjust the choke pull-off opening. They always did as I said earlier and used that vacum source which is basically a small controlled vacum leak as it pulled fresh air from the carb air horn through the exh manifold to heat it and into the choke housing to heat the coil. Almost like a PCV system in the fact that it is a small vacum leak (source) they use and just make up for the small amount of extra air in the carb adjustment. Its always been more or less to me a controlled vacum leak used to draw hot air into the choke so I can understand that it can still be a small controlled vacum leak like was used for years and years on the older carbs. It may be the vacum leaking past the choke piston and if it is not there and the choke thermostat is sealed to the housing then it would just build up vacum inside the choke housing. It may just be to vent the vacum leaking past the choke piston to outside and if thats what they did then they made up for the small vacum leak in the carb adjustment as was done for years. I have not heard of any reason for it to be here to cool the electric choke as that would kinda defeat the reason of what the electric choke coil does. At least I have not seen any electric choke coils need to be cooled after they heat up while the eng is running since most have temp controls in them. Ron

I don't believe I said anything about cooling.

That vacuum operated piston will not work if one side is not vented to atmosphere.

No I did not say it was you but someone else said something about they did it to cool the electric coil as I was refering to them about that.
From a technical standpoint you are right as of course it needs atmosphere on one side for the vacum (low pressure area) to really work since really atmosphere pressure really pushes rather then vacum (low pressure) pulling on anything. But I really dont think that choke cap is sealed that well where the pressure/vacum would even out on both sides of the choke piston so it would not work. All of the carbs like this that I have worked with over the years are the older ones that do not have an electic coil on them as they all used the coil heated by hot air and the vacum that leaks past the piston to pull the hot air into the choke housing. I have not really fooled that close with many of the newer Eddy carbs like this one that use the electric choke with the housing and piston on the carb as this one. The ones I have fooled with are like the ones my brother uses on his dual Eddy carb setup as most Mopars that use well type choke coil and the external vacum break diaphram. But I do agree with you as with any vacum anywhere you need to have atmosphere pressure on the other side to work and the older ones all did since they used the atmosphere pressure side to feed the hot air to the choke coil since the choke piston is not sealed real good in its housing and the vacum leaks past the piston. Ron