Nervous system impairment can be attributed to several conditions in ducks; determining the underlying cause is often difficult, and may rely upon a large amount of the diagnostic tests done by your vet. Working a little bit closer with your vet, asking what things can be done to further diagnose what is affecting him might be the best way to get his condition back into good health.
It may be helpful to see a video of him moving around, as the term "limberneck" should be described as complete paralysis of the anterior neck muscles ( limber neck is mostly associated only with botulism in ducks). Conditions such as wry neck, or opisthotonos are similar in the way of abnormal neck movements, but not in the way that the duck has some muscular control of the neck. In consideration of a possible nutritional deficiency, I think it may be in your best interest to cover more grounds, instead of administering just one vitamin. B12 plays a role in neurological health, but so do a wide variety of other vitamins. Thiamine and vitamin E are two responsible for some neurological health and commonly encountered nutritional deficiencies in birds
That being said, you may consider starting him on a broader poultry vitamin ( there are several on the market in the U.S). Otherwise, giving 1/4 of a B complex tablet, or a few drops of Cattle B complex may suffice. Vitamin E given at 400iu a day may prove beneficial as well.
You have not yet described if he is eating, or drinking much, but when I'm handly a bird in a similar state, it's often best to assume possible weight loss and dehydration. If you have an accurate scale, it would be precautious, to start weighing him daily, and watching his weight. A 5-10% decrease in weight over several days should suggest supplemental tube feeding to maintain nutritional and hydration status. I'm sure your vet could shine light on preforming such a task, but you can so find information on the subject in the link below:
https://www.backyardchickens.com/threads/tube-feeding-ducks-updated-5-7-2020.1211994/
If you could provide some more information on the duck, such as a video of him, pictures of his feces, if you have performed a physical exam, and what you have found that may help us, better help you, although being able to examine the duck, and perform diagnostic tests will greatly improve the prognosis that's why I believe the vet might be your best bet here. If you're not satisfied with what the vet has done, you may try looking elsewhere.
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Jethro passed away this afternoon. Thank you anyway.