I disagree to the idea that the Ring must emit a sort of "signal." We find apparent in
The Lord of the Rings that there are seemingly two worlds - you might even label them "physical" and "spiritual." The Nazgūl evidently have power in this second realm, as do the High Elves and the Istari. Aragorn II had this power too - not entirely physical, but spiritual as well. We find in the Reader's Companion that the Dūnedain sent for him because he was the only one who successfully might resist the Nazgūl.
We also learn from the texts that the Ring seems to have a will of its own. It has the ability to put its wearer one foot - eventually almost fully - into the spiritual realm. It itself seems to have power, but not of the kind effective in the physical. It could touch souls and minds. I think the whole idea of the Nazgūl sensing the Ring's presence is because of the magnitude of its presence in the spiritual realm. Of course if the Ring wants to go back to its master, but is bound to the spiritual realm in a physical object, it might try and contact its master's servants through the same realm.
If this is obvious to everyone already, just ignore me, but I'm not up on the current theories moving across the Downs.
Now, coming back to the main question of why Khamūl could not sense the Ring's presence in the darkness and from such short a distance, I would say he merely wasn't paying attention. He'd been through a lot - fighting Dūnedain, confronting Saruman, getting ordered here and there by the Witch-king and entrusted in finding the Ring. Khamūl might only be able to sense the Ring if he had been paying attention.