I know, for example, that Xzar (?) and Montaron will leave if you take too long to reach Neshkal, but will passage of time matter for anything important, or can I keep resting in the wilderness if I need to?
Montaron and Xzar will leave the party if you don't go to Nashkel quickly enough. Jaheira and Khalid will leave the party if you don't go to Nashkel quickly enougn. Minsc will leave the party if you don't rescue Dynaheir quickly enough. Sam will die if you don't go to the Friendly Arm Inn quickly enough.
Pretty sure that's all.
And the timer is related to in-game time, not real-world time (which is probably why that's what the game tracks).
"...Blame this on the misfortune of your birth." -Char Aznable