On the situation of the Thompson, Cybergun is not one of the better class of manufactures, in fact, they aren't even Cybergun, they are Palco Sports. No offense, but cheap gun + cheap bb's = decent operations.
As for the nozzle thing, IF you think you can do it, I say IF because you really need to be inclined towards this kind of thing, take the gun apart. Pull out the gear box and cycle it through a few operations outside of the gun where you can see what is really going on. In single fire mode, the piston should return to the forward location after each pull of the trigger. This means the nozzle should be in the full forward position as well.
If it is not, take the gear box apart, and be very, very, very careful doing this as the spring is under tension and has a bad habit of popping out and shooting across the room if you are not careful. This is also when half the other parts jump out and now you have no idea where they go.
One technique I use to disassemble a gear box is to remove all but two of the screws, one on each of two opposing corners. Hold the gear box together with one finger of one hand as you remove the last two screws. I generally will push down on the exposed piston casing, it will be the piece that doesn't look like cheap pot metal as the rest of the gearbox does.
Once the last two screws are out, keeping pressure on the piston, carefully seperate the two halves of the gear box, use your free hand and reach in with a finger or two and press down on the main spring to keep it in place. Now remove your finger from the piston and use that hand to remove the rest of the gearbox half.
Carefully remove the main spring from the end of the gearbox opposite the piston, you don't have to take it completely out, just enough to release the tension, leave it in place otherwise.
At the other end of the gearbox, where the nozzle is, you will need to check a few things. First the nozzle itself. Is it broke, or damaged? If not, cool.
Next, the tappet plate, it is a long "L" shape plastic piece that goes from the nozzle back past the trigger and piston and ends at the first gear you come to behind the trigger. Is it broken or damaged? If not, great. There should be a small spring attached to it, make sure it is not broken and that it is attached and that it is also attached to the body of the gearbox. If so, good.
Next, look to see if the tappet plate and the nozzle are properly seated to each other. You do this by checking where they meet. The tappet plate has that "L" shape and the end near the nozzle has a "U" cut out of it, this "U" has a groove in it that the nozzle rests in, if the nozzle slips out, it will not cycle properly. This is most likely your problem.
If all this is good, and everything checks out, then the issue is more than likely your hop up, or your feed tube. Although I'm still betting on the bb's being part of the issue no matter what.
When you reassemble the gear box, do so in the reverse order as you disassembled it. Carefully replace the main spring, holding it down until you can get the gearbox half in place to hold it for you. Keep the piston held down, which will hold the main spring down, and align all the openings on the gerabox with all the "axles" from the gears and the other points in the gearbox. Pay close attention to the anti-kickback lever, it is located generally behind the last and lowest gear in the gearbox. It is a real pain to line up and put back in place if it comes out because there is a small spring that must be in place for it to work. If this is misaligned in any way, your gun will not work right.
Once everything is aligned back up and the gearbox halves mate together seamlessly, hold it together while you replace the last two screws you removed, then once they are in place, finish replacing the rest.
Plug a battery up and give it a test fire, if it works, great, if not, you're going to have to do it all over again to find out what is not in its proper place.
There is a website that has a lot of these gearbox disassemblies on video, I will link to it for your convienence. Otherwise, hope this helps.
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