I think Anti-Light has long been the mechanic behind splintering, or any diminishing of power in a shard.
If a Shard goes against their intent, it might create a small mote of Anti-Light, barely (if at all) noticeable.
But if they are under direct attack, violated in a way that forces them to counter their Intent, Anti-Light is formed, and it hurts them deeply.
Like - Ambition immediately being attacked by Odium might have violated the Intent, and Odium used that against Ambition. This is a stretch, but I’ve been thinking that Odium’s immediate attack would have made him a better candidate in the eyes of the power than the actual Vessel.
Then when Honour and Odium clashed, Odium was always quick to goad him into direct confrontation, even though he had promised not to.
I know I’m stretching - but this theory really comes from Newton’s first law. Put simply, the important part is, “an object in motion stays in motion.”
To stop something, to stop its movement, you need to present force and energy directly counter to its movement. I think it’s similar here - to uninvest something, no matter the means, it’s presenting investiture directly counter to the original. This, I think, is reinforced by how easily the scientists switched their machine from investiture to anti-investiture (calling it Negative Investiture - and I made sure to check that it was in fact Anti investiture, I think they mention that like… a few time? Dunno), suggesting a fluidity that would support this.