This is very implausible, as related. Gold has a melting point of about 1065 degrees Celsius, so melting gold while out prospecting would be extremely difficult. Mixing something that hot with ink is just going to ruin the ink.
Looking at how inks were made before the modern chemical industry, the usual ways were to mix a very fine powder of pigment (fine soot, or iron sulphate and tannin) with a binder, such as hide glue, or gum arabic. Golden ink, as used in Tibet (thanks for those links) would have been made with very finely powdered gold.
Obviously, this prospector would not want to write in visibly golden ink, but mixing very fine gold powder with ordinary black ink would probably work. The difficulty would be creating that fine powder, with particles of about 0.001mm (about 1/20000th of an inch) in size, from a pretty ductile material, under field conditions.
The final problem is that the amount of gold you can hide this way is pretty small, but quite heavy. If you used up a bottle of ink, holding a fluid ounce, you could hide maybe 5-6 ounces of gold.
So, melting is thoroughly implausible, powdering and mixing with ink is more plausible, but quite unlikely.