I would advise against buying gold wire from eBay. How do you know that it is what the vendor says it is.
Also, $45 is not a good price. 6 inches of pure gold wire 24 gauge wire is currently priced at $30 from a reputable dealer (riogrande.com).
https://www.riogrande.com/product/24K-Yellow-Gold-Round-Wire-24-Ga-14-Hard/6081246 inches is .39 pennyweight. A pennyweight is 1.56 grams, so the wire would be .6 grams.
If you could use all the wire (which you could not) you would get 60 doses of 10mg gold.
So the cost would be more than 50 cents a dose.
To make gold chloride, you need hydrochloric acid and fuming nitric acid. You need to mix the two acids in the correct proportion to make Aqua Regia, then dissolve the gold in the acid. These acids are dangerous, especially the nitric.
You would need a fume hood, or do the entire procedure entirely out of doors.
Another method is to substitute high strength hydrogen peroxide for the nitric acid. Some people on the forum have attempted the peroxide method with varying degrees of success.