(So sign 1 is paired with encounter 2, sign 3 is connected to encounter 4, etc.)
Encounters are typically monsters or environmental hazards. They're things that are dangerous, that could damage or kill a character. Other kinds of encounters might be possible, but this is where my process is right now. Signs are meant to create a sense of foreboding. They might be fairly direct clues about the connected encounter, or they might be ominous, ambiguous portents of forthcoming danger.
(If the encounter is the Demogorgon from Stranger Things, the sign might be all the lights flickering on and off. If the encounter is an Agent from The Matrix, the sign might be a black cat that keeps crossing your path.)
|A sign ...|
The first time I roll on the encounter table, I'm not going to distinguish between signs and encounters, I'm only looking to see which connected pair I got. The first roll always produces the sign, and the characters experience whatever warning they're going to get.
The second time I roll on the table, I'm not going to distinguish between pairs. I'm only looking to see whether I got sign or encounter. If I got sign, then the character experience the same sign as before. This can happen as many times as I keep rolling sign. Hopefully, he repetition increases the suspense and foreboding. You know something's coming. If I got encounter, then the characters meet whichever monster is associated with the initial sign.
After the characters finally experience an encounter, I start over, so the next roll always produces another sign.
(You could also be less forgiving than I've described here, and let the first roll give you a surprise encounter. I think that's fair. The dungeon is a mythic underworld; the wilderness howls. Sometimes the only warning of impending danger you get is the knowledge that you've entered a dangerous place. My hope though, is that the procedure I've described might produce more narrative satisfaction, by always foreshadowing encounters before they occur.)
|... leads to an encounter.|
I'm hoping that this approach will help create a world with an active environment, full of strange sights and noises and portents. It has already forced me to focus my encounter tables. Instead of just listing 20 vaguely-related monsters, I find myself narrowing down to 4 or 6 that really help define the feel of the region.
Something like this approach could also work with an overloaded encounter die. These dice typically have two entries for lights going out and magical effects ending, which are typically treated as representing torches and lanterns. You could treat the first such roll as producing a warning - torches flicker or dim, magical effects start glitching and fading. The next time the overloaded encounter die comes back to that pair, you have a 50% chance of another warning (just as the procedure I suggested gives a 50% chance of a repeated sign), and a 50% chance that the lights go out and the magic stops. Just as with my procedure, the goal would be to create narrative tension and satisfaction. The thing is foreshadowed, later the thing happens. In between those times, the thing follows you, stalks you, haunts you. When it happens, it's not a surprise, it's a grim certainty. Or anyway, that's what I'm hoping for.