Let’s imagine a dire circumstance:
You life depends on it
No clock or timer is around
You must wait EXACTLY 60 seconds before pushing the life-saving (or -ending) button.
What method do you use?
Hum the Final Jeopardy song twice. But you’d still be off.
one thousand, two thousand, … , 60 thousand
Have you tested that? I’d go with one one thousand, two one thousand, three one thousand, etc.
Hmm. I tried the “Mississippi” method, but I died at estimating 60 seconds at 58.4 seconds in reality. 
If I had access to a radio , I’d just hope for a 120 bpm song like “Blurred Lines” to come on.
Galileo used his pulse to time the swinging chandelier, and probably many other things.
That’s good enough for me in a pinch.
Mine usually hovers around 60, so it’s doubly useful.
I thought about pulse, but I think resting pulse would be too variable for me personally, especially in a stressful situation like that. I’d probably have better luck estimating off my max heartrate.
Odds are that I’d be dead. I work on this very scenario often. Whenever I use the microwave (which does have a clock that I refuse to look at) I try various techniques to wait out the time for something to heat up. I’m typically off several seconds minimum.
In that pinch thing in the OP, though, I’d hope the one-one-thousand approach would save me. But as one of my favorite lines from One Eyed Jacks goes: “I wouldn’t want to gamble me a handful of brains on it.”
I did an experiment with pendulums and magnets once, as a kid, and noticed that the amount of time it took for air resistance to cause my pendulum to stop swinging (in the control case) was a consistent, exact 30 minutes. Unfortunately, that doesn’t help you and may have been related to the materials I chose, my altitude, etc. as to be largely unreproducible elsewhere.
Somehow I didn’t notice the circumstances.
Mine would be ticking over at 120 or better in a very stressful situation.
Bad measuring tool.
I do a lot of timing when working with my koi pond - timing chemical mixes for testing water levels, timing backwashes, etc. The one-one-thousand, two-one-thousand method is pretty decent for me, but it’s +/- 1 second in 10-second intervals, +/- 2 seconds in a 30-second interval and +/- 5 seconds in a 60-second interval. (Note, I’m often much closer… in a statistical sense, let’s say that these are two standard deviations, to account for 95% of results). That’s good enough for the kind of accuracy I need with my pond, but it’s not going to cut it in this scenario.
The only other things I can think of require effort ahead of time to calibrate a pendulum of some sort - you could even use your own arm as a pendulum. So if you gave me time to prepare to pass this test tomorrow, I think I’d have some decent techniques calibrated to my own body.
My pulse is very variable - it slows down on inhalation, and speeds up on exhalation. I suspect this is true of most people, but in me it is quite pronounced.
I can hear my pulse, always, in my ears. My pulse is pretty consistently around 52, and I can tell when it is more than a couple of beats faster or slower than normal. So I can, even now with the TV on next to me, count my pulsebeats by ear, without needing to feel it with my fingers, and there will be bout 52 beats per 60 seconds.
Even if I check my BP/pulse while watching a sports event in which I have a favorite, it remains below about 55.
I imagine the sound of the stopwatch ticking from the 60 minutes intro which is 4 ticks per second. I’d always used that sound memory but wasn’t sure how accurate it was. I just tested with a stopwatch and I was accurate to 1/4 second over one minute.
Go have sex. Twice.
I sing to myself a Sousa march (my favorite is Liberty Bell - the Monty Python theme), and repeat it once. I was in marching band so we were taught to step at 120 steps per minute, so I tap my toes doing it. The stanza is 32 seconds long, so you need to stop before the last measure.
I’d guess.
I just sang the 50s song “Lollipop” and the beat in my head turned out to be very close to a second each finger snap.
I count to 60. One, two, three, four, etc… I’ve been doing it for decades and I’m pretty accurate from practice.
I seem to remember that the characters played by Bruce Willis, Danny Aiello in the movie Hudson Hawk would sing songs to keep in time when they were separated from each other.
In keeping with the mundane pointless stuff theme - Before GPS units were allowed during rounds of golf, I would count my strides from the tee to where my ball had landed. 100 strides = 90 yards, 200 strides = 180 yards. It was useful to determine the remaining distance to the green.
There are exactly 10 inches between the extended tip of my little finger to the tip of my thumb, on either hand. The distance from the tip of my middle finger to the base of my palm is exactly 8 inches, and my palm is exactly 4 inches wide. Useful stuff when measuring rope or judging window and door sizes when a ruler wasn’t handy.
OK, then what will you do for the next 30 seconds?
Probably best to stop then, if only to avoid the giant foot.