Johannes Schmidt spent years towing plankton nets across the Atlantic and mapping where the smallest leaf-shaped leptocephalus larvae turned up. The smallest were found in the Sargasso Sea, so that is where he placed the spawning ground. The conclusion was drawn from a gradient in larval size, an indirect argument that has stood for a hundred years.
Modern satellite tags attached to migrating silver eels have tracked animals leaving European rivers and heading out into the Atlantic, and released data support movement toward the Sargasso. Naturally spawned eggs of Anguilla anguilla have not been collected in the wild, and no adult has been observed spawning there.
The gaps matter for conservation. Eels cannot be reliably bred to a self-sustaining commercial cycle, so every farmed eel begins as a wild-caught juvenile, which makes aquaculture a draw on the wild population rather than a relief from it. How long the migration takes, what route the eels use, and whether spawning is concentrated in time are all still argued over.