There are lots of gotchas with that carb but also many reasons other than carb that a 404 mog will not start and run properly. Getting fuel to the carb is the first place to look. Disconnect the line at the carb, crank the engine and watch for fuel. If none then clean the primary fuel filter (bowl type) near the front tank, the filter in the fuel pump (left front bottom of the engine), verify a good fuel pump cover gasket (those were cork and get brittle and leak). Verify the tank selector valve is oriented either pointing rearward (rear tank) or 45 degrees to the right rear (front tank). The 90 deg position (toward trucks right side) is OFF.
There is a manual priming pump on the fuel pump. Pump until you get fuel to the carb. If the pump does not seem to be working then rotate the engine to take the fuel pump push rod off the lobe on the crank. If the actuating rob is already pushed then the manual pumping can't work.
With plenty of fuel then move on to the carb. That's probably the normal Zenith 32NDIX carb. Since it was rebuilt, one possible problem is that this same carb model was used on many vehicles, including Porsche, and a rebuild kit for that 'model' probably came with the wrong accelerator pump piston/rod. The Unimog used a unique length. If the running problem involved typical 'dead spots' when trying to accelerate then there's probably a wrong accelerator pump piston.
The choke system on the 32NDIX is very different. The choke circuit is a separate enrichener circuit. There is no typical choke function involving partial closing of the butterfly valve. So, if the choke was not reassembled correctly the choke does not work.
Technique: Never push or pump the accelerator pedal when starting. Don't touch the pedal, just apply choke (enrichener) and crank it. It should start immediately and then you start reducing choke but still apply no pedal. As choke goes off, then use pedal as needed.
You can emulate a normal choke by putting your hand over the carb throat. Ovoid flaming gaseous backfires if possible
When the choke is operating properly there will be a strong sound of sucking air coming from the carb after the engine starts. If you don't hear that sucking of air through the enrichener then you probably need choke work.
There are only two adjustments on the carb, the two air circuits for idle. Idle fuel is set by jets, but these jets can plug easily. If you can get the engine running, and try screwing either idle air adjuster inward, if the screw bottoms out (gently) without making much difference in how it (poorly) idles, then the jet is plugged.
There are also two easily changed (and plugged) high speed jets which should be checked.
All four jets are located in the front of the carb under a removable cover. You first picture shows part of it, and half the 10 mm screw. You can reach the cover by reaching back in the engine compartment over the grill. Use a 10mm wrench to remove the cover screw. Check the cover's o-ring. On a rebuilt carb the o-ring should be perfect.
Use a screwdriver to remove the jets. Remember where they go to prevent headscratching later. Two jets, the high speed ones, will have a number stamped on the head end. 140 is normal for sea level to 5k feet approx.. 130's or 125's, etc, would be used for higher elevation.
Visually check the idle jets for plugging. The holes are tiny and damaging them with a probe would be bad. Carb cleaner works, as does air jet. Gently blow out the holes where the jets came from, too. On the idle jets, you will find a hole axially into the end which terminates in a cross-bored hole. Check both.
When you put the jet cover back on, look for the word OBEN written on one edge. That goes to the top. Installation upside down will allow leaks but can damage the socket where the screw threads in, too. Only tighten the 10mm screw gently. Let the o-ring do the work.
Let us know how that works out.
That's a cool hardtop Unimog 404. There are not many with a radio box on the back, most being fire apparatus. I'd really like to see some interior shots of the box if you get the opportunity.
Bob