Watching this image used in this question Why would astronauts in SpaceX's Crew Dragon need two separate timing devices: one portable digital timer, and one wristwatch, rather than carrying into orbit only one of those seemingly equivalent time keeping devices?
(Shuttle-centric answer, but concept likely applies to other spacecraft, especially involving crew who flew on the shuttle)
"Egg timers" were utilized heavily on the shuttle to time multiple things going on at the same time.
For example: A crewmember wants to check something a minute before a burn. The flight software timer is counting down to the burn time itself; the timer is handy to set an alarm for the memory jogger.
(The shuttle cockpit had built-in "Event Timers" but they were not as convenient to use as the egg timers)
All kinds of procedures on shuttle had time intervals built in, and sometimes were run in parallel. In sims with a lot of failures, there would be several egg timers going at once.
Here's one where the crew almost always used an egg timer in training: This APU COOLDOWN procedure was run to prepare a recently shutdown Auxiliary Power Unit for restart. The RESTART procedure has 1.5 and 3.5 minute checks in it.
(from the Ascent / Entry Systems Procedures)
Here's an official NASA photo showing the late Alan Poindexter training in the Shuttle Mission Simulator, with an egg timer highlighted.
As mentioned in another answer to your question, astronauts may need to time multiple events. Also using multiple clocks helps to detect if one clock is wrong. In fact Buzz Aldrin famously wears three watches, he says one reason is because with only two you don't know which one is right, whereas when wearing three watches they essentially "vote" on the correct time.
“See you need an odd number (of watches) in case there is a discrepancy so you can sort out which one is what,”
And similar to airline pilots who sometimes wear two watches for different time zones, astronauts often wear two watches for the same reason. For example one watch set for UTC, the other for MET (mission elapsed time). Some astronauts also like to have a watch set for central time which is the time zone for Houston where they live and work.
However you specifically mentioned timers and wristwatches, and this brings up another reason which is utility. Since the beginning of the space program astronauts have worn watches because spaceflight is carefully choreographed and scheduled, and it is vital to know what time it is so that activities can be done on time, as well as estimate the time remaining to complete a task. Like on Earth, wearing a wristwatch ensures that the correct time is always less than an arm's length away.
Wristwatches are also used on EVA's (spacewalks and Moonwalks) for the same reason, situations where using a regular clock or timer would not be feasible.
Alan Shepard, Apollo 14 EVA-1, photo taken by Ed Mitchell from the Lunar Module (NASA ALSJ)
On the other hand (no pun intended), when inside the spacecraft performing various activities such as conducting experiments, or robotic arm procedures, or rendezvous and docking maneuvers, when the astronaut will be mostly facing in the same direction, it can be helpful to have a timer in a fixed position in front of them which can be glanced at without having to move their arm or turn their head away from the task. The larger numbers on a timer are also easier to see, and the buttons make it easier to set.
This is also true during launch and reentry. The following image is a screenshot from a video of the launch of MS-09 on June 6th, 2018. On the Soyuz instrument panel the two cosmonauts and NASA astronaut Serena Aunon-Chancellor each have a CDN egg timer velcroed in front of them.
As CourageousPotato mentioned in a comment:
You can't have enough clocks in space travel; accurate timing determines whether you can execute precise maneuvers at all.
To build on this: not all clocks are created equal. Some are simple - they were set to a starting time, and tick up when their internal workings cause it. Some are more complex - atomic clocks, clocks based on satellite signals, etc. Clocks may be calibrated on the ground and provide reference points to gauge the accuracy of other clocks.
Having multiple clocks may help build consensus when different time sources fall out of sync, somewhat akin to bit voting/data deduplication/n-versioning in software engineering. This is especially useful when you have multiple clocks that all used the same calibration. Real-time clocks are a class of technology and R&D all on their own.
Speaking as a pilot who uses egg timers in the cockpit one of the primary reasons is convenience: they are quick and easy to set and change, whereas setting timers on a watch are actually a real pain in the butt.
With a watch the timer set process is something line this:
- Press mode three or four times
- Hold down a button for three seconds to initiate set mode
- Press and hold an up and/or down button to set the hour
- Press mode to change to minute
- Repeat step 3 to set minutes
- Press mode again to change to second
- Repeat step 3 to set seconds
- Press and hold a button for 3 seconds to exit set mode
That takes about 30 seconds at best, now imagine doing that with one hand while your watch is strapped to your other hand, while that hand is flying a plane, in cloud, in turbulence. And, by the way you need a 30 second timer and it takes longer to set than what you wanted to time.
Whereas a kitchen timer takes about two seconds to set. If I want to set a 1 minute 30 second timer it's: clear-1-3-0-start.
Other benefits of egg timers over watches for timing in the cockpit:
- The screens are big and easy to read, watch displays are much smaller
- You can position the timers where they are in your field of view while you fly your spacecraft or airplane, having it part of your regular instrument scan. If it's on your wrist you have to look down
- You can have as many as you like, even if you have multiple timers on your watch they don't display at the same time