creating time pressure outside of travel

hey all - I'm working on putting together a Cairn one shot for my table. it's a pretty sandboxy mystery scenario, with consequences if the characters don't unravel certain threads after a few in-game days.

I really like the watches mechanic as a lightweight way to track time passing during travel segments, but since most of my game will take place in a single town, I'm looking for ways to create a sense of urgency during social encounters and investigation.

do y'all have any systems you like using? maybe even ways to adapt the watch mechanic to non-travel segments of the game? I'd really like to keep things simple and fiction first, but tense.