Are there established rules in GURPS for sleeping monsters/people/whatever being awoken by things going on around them? There doesn't appear to be any such thing in Campaigns, but I didn't do a paragraph-by-paragraph search.
The executive summary: Sleepers wake when their sleep is disturbed, which happens when un-stealthy activity occurs nearby. Sleepers whose sleep is disturbed only rouse if they perceive a disturbance as a threat, which is determined by a test of IQ.
Due to the wording in Deep Sleeper that says they get an IQ roll to notice a dangerous disturbance and wake, "just like anyone else" (B101), a sleeping character rolls IQ to rouse when a disturbance is made. This lines up nicely with the rules for recovering from surprise (B393): a sleeping character suffers Total Surprise, until they succeed at an IQ test. (Light Sleepers (B142) have extra rules for what wakes them, which make it far easier.)
However, with the obvious exception of noisy combat, you first have to determine if a disturbance is made. For situations like attempts to stealthily infiltrate a room/camp full of sleeping people, test the intruder's Stealth, and only when they fail a roll do they cause a disturbance that grants an IQ roll. (They automatically fail if they don't attempt to be stealthy!) This isn't opposed by a sense roll because Quick Contests require two active participants, and sleeping characters are the opposite of actively alert (Total Surprise, B393), with the exception of characters with Combat Reflexes (ibid.).
Since succeeding an IQ test meaning waking up to a harmless disturbance is counter-intuitive (and GURPS is all about implementing internally-consistent reality and fantasy), you might wish to re-purpose the IQ roll for determining if they sleepily deduce the nature of the disturbance accurately. A real-life person whose sleep is disturbed (not yet fully interrupted) will not rouse if they perceive the disturbance as harmless; handling it that way will allow your players to possibly avoid unnecessary penalties for missed sleep (B426) from harmless disturbances. Handling it like this, a successful IQ test means they react appropriately, while a failed IQ test and a dangerous disturbance would mean they roll over and go back to sleep, and a failed IQ roll and a harmless disturbance means they will rouse in false alarm. (As with all rolls in GURPS that determine what information to reveal to a PC's player, such IQ rolls should made by the GM in secret.) The exception is that a character with Combat Reflexes automatically succeeds on the IQ roll.
Effectiveness after rousing follows the normal rules for being surprised (B393).
Page 101 of the Basic Set, Character
Page 5 of Dungeon Fantasy 2, Dungeons.
The main difference between the two is how Combat Reflexes are handled.