What would the path be had you been able to contain the light?

[Enkidoh]

It was never explained alas - all we know is they resigned and the seat of Azem was never refilled, with the rest of the Convocation continuing on as normal. And their resignation was treated more as a betrayal, which is why the Convocation never made an actual memory crystal for Azem, regarding them as a traitor undeserving of their memories to be saved (essentially making them 'persona non gratia') meaning the WoL could never be hypothetically 'raised up' back to the seat of Azem as an Ascian even if they wanted to (Emet instead deciding to make a special one behind the Convocation's backs for his friend, filling it with their 'signature spell' of group teleportation to them instead of others' memories of them, and giving it to the reconstructed shade of Hythlodaeus in his Amaurot reconstruction to pass onto the WoL.).

My headcanon is that Azem refused to lay down though and took the third option which was continuing to do what they do best: travel the world helping people and fighting monsters, even without the power of the Convocation behind them. So I believe they probably continued to fight against the Terminus beasts and saving people from the disaster.

Furthermore, this is what I think the Amaurot dungeon in ShB actually was based on - as EW showed when the Final Days finally arrived in Amaurot, Emet didn't fight (and neither did Venat), all Emet did was stand out in the street talking to Hythlodaeus while the world went to hell around them, attempting to convince his "other old friend" not to join the initial sacrifices for Zodiark's summoning (and then probably teleported out to join the rest of the Convocation in the summoning rite), but during that he probably noticed Azem stubbornly fighting on, slaying Terminus beasts as they materialized and saving what victims they could. And thus, he wove that into the 'theme-park ride' of Amaurot's fall, basically rubbing the WoL's face into how poorly they measure up to his old friend.

Of course I have no actual proof of that, but it certainly fits.