In [TEOTW: Prologue, Dragonmount, xi], Ishy visits LTT after he kills his family:

Elan Morin grimaced. "Look at you," he said scornfully. "Once you stood first among the Servants. Once you wore the Ring of Tamyrlin, and sat in the High Seat. Once you summoned the Nine Rods of Dominion. Now look at you!"

Scott Mocklin tells us that the new glossary in To The Blight (vol. 2 of the YA version of TEOTW) has the following entry:

Ring of Tamyrlin (TAHM-ehr-lin): a legendary ring, believed mythical by most people, worn by the leader of the Aes Sedai during the Age of Legends. Stories about the Ring of Tamyrlin include that it was an angreal or sa'angreal or ter'angreal of immense power. It supposedly was named after the first person to learn how to tap into the Source and channel the One Power, and in some tales, was actually made by that man or woman. Despite what many Aes Sedai say, no one knows whether it was a man or a woman who first learned to channel. Some believe that the present title of Amyrlin is a corruption of Tamyrlin.

Which pretty much matches previous speculation about the word's origin.