You are all over this question. Thank you for such an expert and quick response. I am curious as to why I don't see this on many videos or photo of other 56's? Do they have a different means of warming up the carb?It so happens we were just looking at this part on my 56, but it has the factory-installed style of this tube (short, goes basically straight down just a few inches into the manifold). This is part #9820, on p. 4194 of the Parts Manual, Thermostatic choke control inlet tube.
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No drilling work that I know of. The previous owner had the car for the last 40 years and had no work done on the manifolds. Could there be a filter of some kind to prevent soot or other debris from reaching the choke?Looks like shreds from a drilling operation. Had any work been done recently?
Neither pictures above is correct for a 56 Bird. The second pic is for a 57. The first is a later modification using a later exhaust manifold. Also note that there is a second tube on the drivers side that attaches to the crossover tube in the intake manifold that goes into a hole in the carb body
All this is if you have the stock carb.
After I had my engine replaced 30ys ago I neglected to re torque the heads after break in. Blew a head gasket and had to pull the top end. Replaced my heat tube in the process as I had the intake manifold off anyway. .Quite interesting. From what I see on the parts diagram combined with what you just outlined it seems to me what's shown as the "service installation" parts were to fix the problem you described, the tube burning out and clogging. In the left side where they show the production parts they make a distinction between the 56 parts and the 57 parts which I presume is because the 56 used the teapot and the 57 used the holley. The "service parts kit" has plugs for where that burned out tube went across and a replacement "heat stove" to put down on the exhaust manifold. All of which to presumably make the repair quick and easy with no need to remove the manifold.