If you're going to use any injectable gear, then of course you're going to need some "darts." You can pick up syringes at your local pharmacy unless your state has certain restrictions. Also, you can purchase needles online. Just do a little searching around and you'll find several places that'll hook you up. Syringes will run you around 50 cents apiece. Note that it'll be more difficult to obtain needles (at least from the larger, more "legit" companies) if you live in California and Illinois. You'll usually need a doctor's prescription in those states. Still, if you look around enough, you can get what you need.
The vet can perform a Tarsorrhaphy by injecting the eyelid with a local anesthetic and sewing the third eyelid shut. At the same time the vet may inject a mild antibiotic directly into the eyelid. The third eyelid in a goat has a gland which provides some immunological protection and helps increase the blood supply to the eye. Stints (small pipettes through which sutures will be threaded) and dissolvable sutures will be used to hold the eye closed for 10-14 days, allowing the eye to stay moist and healing to take place. The stints used to hold the eyelids together can easily be cut loose from the eyelid with small scissors after the sutures have dissolved. Obviously you don't want to use this procedure on both eyes at one time.
My puppy (chihuahua Yorkie mix)started scratching his eyes when he was about 4 months old. I took him to the vet and he scraped him and said it was demodectic mites. He was treated with bravecto to kill the mites and a antihistamine because of his constant scratching. In about 2 weeks he started to re grow the hair around his eyes. He was re scraped 2 weeks later and showed no mites. A few weeks after that he was back at the vet for scratching and losing hair again. He was again scraped and since it had been 2 months since the first bravecto treatment he gave him another bravecto pill and an antibiotic because of infection and a stronger antihistamine. It has been 2 and a half weeks and his eyes are worse and his scratching has not stopped. I am thinking that the cause is not at all demodectic mites. Could it simply be allergies? Poor baby is always scratching and now starting to make the skin around his eyes raw.