There are many choices on the road to earning a fortune of gil in Final Fantasy XIV, the most important of which is the methods you'll use to make money. The activities you use to earn gil need to be enjoyable, and for those who regularly participate in FATEs, using Bicolor Gemstones is an obvious choice.
Bicolor Gemstones are a currency tied to the Shared FATE system introduced in Shadowbringers. Completing a FATE within one of the Shared FATE zones in both Shadowbringers and Endwalker rewards a specific number of Bicolored Gemstones while progressing your Shared FATE rank. With each Shared FATE rank completed, a new tier of rewards is unlocked through the Bicolor Gemstone trader in that zone.
There are plenty of rewards to earn with Bicolor Gemstones, like minions, chocobo bardings, orchestrion rolls, and mounts, which means there's plenty of potential money to earn as well. Earning a substantial amount of gil will have you see many FATEs in your future, but by having the proper goal to work toward, you'll see the results of your labor in no time.

How to earn gil with Bicolor Gemstones in FFXIV
The more attractive items earned with Bicolor Gemstones, like minions and mounts, aren't tradeable, so unless you'd like to add them to your own collection, they won't be your goal. Instead, your focus should be on the many crafting materials, furnishing items, pre-Endwalker orchestrion rolls and Bicolor Gemstone Vouchers sold by the various Gemstone Traders to put on the market. If you have an abundance of Bicolor Gemstones that you're itching to trade, what to sell may not be obvious when starting out.
Buying and selling crafting materials
Many of the crafting materials sold for Bicolor Gemstones cost one or two gemstones each and only require the first Shared FATE rank to be unlocked — you only need to have completed one FATE to reach rank one. Since Shared FATEs reward 12 Bicolor Gemstones, the market boards are likely already filled with similarly-minded players' listings for them. You can use sites like Universalis to research what items sell quickly despite the competition and how many other players usually buy. There's a chance you could edge out the competition by putting in the extra effort and gemstones to sell stacks of 99 rather than what you can afford.
Furnishing items and orchestrion rolls
The more Bicolor Gemstones are required to exchange for an item, the more likely it is to translate into a high market price. Gemstone Traders in each zone carry a combination of furnishing items and orchestrion rolls for upwards of 350 gemstones, and these items are locked behind the second and third Shared FATE ranks of their zone. Since many players likely have their eyes set on one of the other goals Final Fantasy XIV offers outside of Shared FATEs, completing 66 FATEs in one zone sounds like a lot of work. They'll throw gil at the market board to bypass the effort involved, and you'll start fantasizing about diving into your newly-earned pile of gil like Uncle Scrooge.

While any furnishing item will sell eventually, some are much more desirable than others, according to the economy. You can find the most popular furnishing items that will sell on your server by doing some light research using Universalis and the in-game purchase history. That said, the most popular items will likely have the most competition, so be prepared for a lot of price changes and undercutting. In addition to furnishings, orchestrion rolls purchased from Gemstone Traders in Shadowbringers zones fetch a high price on the markets, but those introduced in Endwalker's Patch 6.0 and onward aren't tradeable. Not everyone is rushing to complete their orchestrion roll collection, but collectors browse the market board daily.
Bicolor Gemstone Vouchers
Bicolor Gemstone Vouchers are the most likely item to earn you a profit, regardless of which server you're located on. The price of 100 gemstones per voucher may seem like little compared to furnishing items, but the requirement of reaching the third Shared FATE rank in each of Endwalker's six zones makes the cost much more hefty. With 66 FATEs required to reach rank three in each zone, that's 396 FATEs between starting and purchasing a Bicolor Gemstone Voucher.
What makes these vouchers so desirable is that you can exchange them for a rare mount or a winged fashion accessory. The catch is that to unlock the Wivre mount and Fallen Angel Wings, you'll need to exchange 500 Bicolor Gemstone Vouchers, equaling 50,000 Bicolor Gemstones or otherwise nearly 4,000 FATEs worth of work. Thankfully for the mount collector and yourself, the vouchers are tradeable. Rather than try to earn everything themselves through a never-ending FATE grind, players will buy as many vouchers as they can afford to shorten the time they spend earning the rewards.

By selling your Bicolor Gemstone Vouchers, you're forgoing any progress you would have made earning the two items yourself if you haven't already. You can wipe your eyes with the bank notes you earned from your Bicolor Gemstones and reverse the roles by buying the vouchers for yourself someday. The mount and wings themselves are both tradeable as well, though any asking price for them has an immediate impact on your funds rather than the paced progress of buying vouchers.