The GM narrates the outcome of the roll. He says what happens, and then adds “I’m adding two ticks to the X clock” to represent that.
Then, we assume competence and insight on the part of the characters. That they have intuition related to the situation they’re in that goes beyond our imagined intuition as we sit at a table looking at numbers on paper and talking to friends and rolling dice.
I mean… have you ever been in a situation where, despite the fact that there’s not some visual countdown available, you got a strong sense of some pending thing happening?
Are you surprised by everything that happens that’s not scheduled beforehand? Are you just wandering around in a perpetual state of shock as things happen suddenly around you? Or do you observe the world around you and draw conclusions about what may or may not happen, and when, and then consider things accordingly?
My own personal experience with this is that while I might sometimes get a sense of some pending thing happening, the achieved accuracy of that sense both in outcome and in timing ranges from mediocre to abysmal.
Given that, I don't assume any greater degree of intuition on the part of my characters until-unless something in the game tells me I can; on which the fiction becomes that much less believable.
You just narrate additional information that reflects an increase in whatever the clock represents.
It’s that simple.
As a player, the narration of slowly-approaching doom (if done at all well) would or should be enough for me to roleplay the increasing stress being placed on my character. A player-facing clock or counter would a) needlessly add out-of-character stress on me-the-player and b) make that sense of impending doom far more accurate in terms of timing and-or nearness than seems believable.
Because the clock is representative. Just as with all mechanics. Does Conan know that he has a 20 Strength? No. Does he know he’s stronger than Subotai, who has a 12 Strength? Yes. Is it Meta that he knows that? No.
Conan might, though - were he more math-and-stats inclined - have all the other warriors he meets, plus himself, test their strengths* against each other and then come up with a rough numeretic scale to represent how strong each warrior is in relation to the others and to himself. It wouldn't be a nice neat 3-18 bell curve, of course, as that's supposed to cover the whole population rather than just the elite warrior types, but it'd still be a numeric representation of relative strength among those he hangs out with within the fiction he inhabits.
Hard to see how the same could apply to a clock where the characters can't necessarily see or know what's coming, or how far off it is.
* - something less easy to objectively test and compare, such as Charisma, would suit your point better, as at least some of that is in the eye-ear-head-heart of each individual beholder.