Hi, I’ve got a 2001 concours that I fixed up. I bought new needles and bowl gaskets for the carbs. I cleaned them very well. Removed everything and cleaned all the passages including the choke plungers. I checked all the passages. I’ve been through the carbs several times. If the air is fairly warm(70f)it will start with a bit of effort but once it warms up it runs amazing. The problem is the choke doesn’t work. I grew up working in motorcycle shops and have rebuilt lots of carbs. I’ve never had a problem like this before.  Idk maybe someone here might having something insightful to say. Thanks.

On the C10 carbs it is a Fuel Enrichment system, it is not a choke.
A choke restricts airflow to make the fuel-air mix richer.
The system fitted to the C10s Keihin carbs adds extra fuel instead.

If pulling the lever pulls the 4 plungers open but makes no difference then you either have a blockage in the fuel supply to the plungers or else the carbs are already running too rich and opening the plungers is supplying too much fuel.
Also make certain that upon closing the "choke" all 4 plungers go back into the carb.
I saw one set a few years back where the return springs were so weak that the plungers stayed open.

In the bowl area near the top, there is a hole below each of the Enrichmemnt valves.

I had the same problem you're describing, and it turned out that one {or more} of those holes was stopped up.

Ride safe, Ted