There’s a WoWhead comment (https://www.wowhead.com/classic/item=17780/blade-of-eternal-darkness#comments) that mentions:
“As of hotfixes June 19, 2020 Blade of Eternal Darkness will no longer proc from non-damaging spells in WoW Classic”
There is another comment from later that same year (2020/12/26):
“From what i have seen it does not proc on blizzard (not even the first tick, never seen it proc of blizzard)”
It appears that it likely does not proc on DoTs, and Blizzard is a damage over time effect.
