I know the sort of box you mean, but I associate these with earlier wiring, often VR. I think I've even seen them used with lead sheathed, and some with cable clamps as well.The joint box is usually on the landing, just at the top of the stairs…. But as above, you’ll need to lift carpets and boards to find it.
It will be a square or rectangle plastic box with all the grey twin and earth cables running into it.
I reckon this is more likely to be a round 4 terminal box with a screw on lid and used one per light.