The technique that I use for force-feeding is to use the back of my left hand to hold them down in their nest (you can also wrap them in a towel if need be) while cradling their head between the middle and ring fingers. You need to extend the neck and head from the body (straighten it up) if you're going to tube feed all the way to the crop. You take the fingernails of the right hand and pry the beak open and then use the unused fingers (index and thumb) of the left hand (that's still upside down holding the bird's body down while cradling the head at extention) to hold the beak open while you either roll seeds down or insert the syringe.
If you pick a line of insertion that points the tip slightly towards the back of the throat as it's going past the opening to the trachea (airway), you won't have a problem with that. It's also a little better to insert the tube on the left side of the beak (the bird's left) and cross it a bit to the right side (the bird's right) as the esophagus goes down the right side of the bird's neck (the bird's right).
Most birds will struggle, some ferociously. The authority with which you hold the bird is very important. If you let them struggle too much, you'll either chicken out and the bird won't get fed; it'll be a real sloppy job with food all through the mouth, crop and esophagus possibly resulting in the bird breathing in some food (aspiration) and getting very sick or dying (sometimes immediately); or you can hurt the bird's esophagus to the point of rupture in the extreme. You just don't let the bird struggle. If they're going to play rough, then you wrap 'em in a towel for restraint.
If you're in doubt as to getting it down the airway then first open the beak real wide so that you can see where the airway is and how it's situated. It's a longwise oval slit just behind the base of the tongue. It can close completely. If you're desperately afraid you're going to go into it, then make sure the tube is clean before you go in, insert it some ways and then hold the bird's beak open enough to look in and make sure you've got it going the right way before you start pumping stuff in. After you get used to the technique, it's pretty quick and easy.
The "equipment" that I use is easy to get from a store like Home Depot, Lowe's or other hardware stores. It's simply electrical heat-shrink tubing that is generally used to slip over a portion of bare wire that you want to cover and then heat with a blow-dryer-like device. That causes the tube to shink. For our purposes here, there's no need to shrink it--you just pick the size that can be slipped over the nose of a syringe you're using and start using it. I usually do almost heat the business end to shrink the very front (the end that's leading the way down the pigeon's gullet) just to make it bullet-nosed but that's not necessary. It's pretty easy to overdo it when you're heating the end but you just almost but not quite touch it to a lit match for the splittest of seconds. Anyhow:
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