Unless you know how to retrieve gold from scrap or know a certain piece of Unknownum is the karat gold you need and want, you are much farther ahead just buying a piece of 'sheet stock' gold in the karat and thickness you need for the job.
When you buy this stuff, nearly always the thicknesses will be expressed in Brown& Sharpe (B&S) Gauge numbers.
Jewelry and sheet metal work uses this gauge thickness system.
After a while you get used to it and know what your common use gauge B&S matr'l is in .000" thickness. Just like working with Metric/English.
There are other simple conversion charts on the web as well.
When ordering gold and silver wire for engraving inlay I would always order 20, 22, 24, 26 & 28 gauges
That would cover any inlay work as well as figure work as I use the wire to build inlays.
For sheet gold on a project like this,,just decide what thickness you want to use in .000"
Look up what the B&S gauge of the matrl will be,,or close to it.
Order that thickness or maybe you want one size thicker to be sure of enough matrl.
You order by the karat ( 24k in this instance I would assume)
Then the thickness of the sheet..the B&S gauge
Then how big a piece...
You can usually tell them to cut a piece to your specific demands if they are simple square corners.
1" x 1" for example.,,1/2" x 3/4",,,1/2" x 1/2",,,what ever you need.
They may have a minimum but I've never run into that. At the price of 24k,,it'll be plenty $$ anyway!
Put it on a charge card and wait by the mail box.
Even 24k they may ask if you want it 'annealed'. Sure.
I often anneal it quickly with a propane torch anyway.
I've used T.B Hagstoz for the last 50+ yrs.
https://hagstoz.com/contact/Scroll down to the bottom of the page for an 800#
Lots of people use RioGrande Jewelry Supply
https://www.riogrande.com/Most engravers/jewelry makers have a favorite they've stuck with over time. Gold is gold and the market sets the price. It changes every day, sometimes every hour.
So you won't often find posted prices listed for gold wire and sheet stock. You have to call to order.
RioGrande usually has the Market price of (pure) Gold listed but that's not what you pay anyway...you pay more!