It is not about how many echoes you do or how much you clear them.
Just to be clear, the target farming aspect from specific timelines comes from exclusive Echo Reward Nodes, that only spawn in these respective timelines.
There is no extra chance for random drops inside the echoes or such.
These Specific Unique/Set Item Echo Rewards are relatively rare, but there are two things that you can do to imrpove the chances of them spawning:
- The Depth of the Echo (how far away the echo is from the starting point)
- Corruption in this Timeline
So what yo uwant to do is, go as far outwards as possible in the echo web.
Echoes with rewards that don’t interest you can be completed as quickyl as possible, you don’t need to fill stability, just complete the objective. The sole purpose is to reach more echoes, more far out in the echo web.
Extra tip: If you come across Vessels (both Vessel of Memory and Vessel of Chaos), do not do them immediately.
Uncover more of the echo web and use them before you are about to reset the timeline with a Shade of Orobyss kill.
With the Vessels you can exponentially multiply your rewards from specific desired echo rewards.
I made a guide on this a while ago. I do think it is a bit overkill fo an Item like the one you are looking out for, but once you want to farm that item multiple times to have LP this will become mroe useful.
EDIT: Also you should try to do this on Empowered (Level 100) Monolith, as these nodes are very very rare on normal.