Let me see if I have the concept right. It's an elephant carving that makes good parents try to hurt their kids. If the parents resist, the mother immediately goes into labor and has a genius child. Is that right?
If so, I had trouble understanding this. The article seems to contradict itself many times:
SCP-4390 main anomalous effect is that when touched directly by anyone with biological or adopted children, their body will undergo an extreme compulsion effect, except for leaving their mind and eyes unaffected, and will become an instance of SCP-4390-1.
…
In the presence of adults, SCP-4390-1 is nearly indiscernible from that of a normal human adult, other than sporadic eye movement.
So touching it secretly changes someone into SCP-4390-1, right? And they only change around kids?
Well, when the agent touches it:
When SCP-4390 was intially touched by Agent █████, she immediately had a violent seizure, and began omitting expletives while begging for help.
Furthermore,
[The agent] gave birth, despite Agent █████ not being pregnant.
Which is not listed anywhere in the description.
D-03821, Single, Female, One Biological Child, 15 years of Age. Charged and found guilty of three accounts of murder. Positive Relationship with her child.
This testing format is also confusing. Are they testing these people on their own kids, or on a random child?
For the idea in general, there are many objects that compel people to be violent, and this concept doesn't stand out to me, especially compared with other entries like SCP-089, where parents must choose of their own choice to hurt their children.
You specifically asked for feedback on the 'unfinished' testing format. I think that concept could work in a different article, but in this article, it seems more like you just didn't finish it as an author.