How are amulets linked to shield guardians? Is there a magic ritual needed to link the construct to the amulet? Also, does the amulet have specific resources needed to craft it other than having to be worth at least 1000 gp?
It is open to DM interpretation. There is no official word on the matter, but in my experience DM'ing it's a good thing this was not rigidly defined.
I've had magic-scarce settings where these sorts of things were relics of an ancient and extinct race, containing magic that could not be replicated by today's scholars or requiring materials that have become so rare they're considered fictional.
I've had high-magic settings where these are craftable (I often require either proficiency in Jewelcrafter's Tools and Arcana, or make it only craftable by an Artificer). I've set different rarities of amulets that have different requirements for creation, use, and effectiveness. Some of theme require channeling magic into the amulet for a set amount of time. Some of them require to be made from part of the shield guardian, and certain levels of spell slots are required to be "expended* to bind them to the construct.
The only set rule out there is the one you referenced. Presumably, you can make an amulet out of anything you want, so long as it costs 1000 GP. It could be a plain-looking amulet, or a brilliant shining amulet with inlaid gems.
That's in my own experience, and I'm happy it is not defined. Now, I'm entering the realm of opinion here, but I feel it's best to not have an official word on literally everything in 5e. Work with your DM on ideas like this, or if you are the DM, use the loose definition as an opportunity to get creative and flavor the shield guardians and their amulets to your setting.