How did monks time their practice? How did monks traditionally time their practice before the age of timers?
Any sutta references would be greatly appreciated.
I'm looking for an organic way to time my sittings.
To refer to the traditional way that time is kept:


  "The best way I've heard to a) keep track of time b) without a clock
  (or timer) was related to me by my 91-year-old teacher who said in the
  old days they used to use incense sticks; once the incense stick was
  finished, they would switch from walking to sitting. For shorter
  sessions, you could cut the sticks in half, etc. Of course, it still
  means you need to open your eyes every so often during sitting."
  --this answer


The act of not timing your sitting is a profound one. It's not like the Buddha timed his sittings when he attained Enlightenment!
After nourishing himself the Buddha himself literally said "I will not get up from this Bodhi tree until I attain Awakening! Let my bones break and my flesh rot before I shall arise."
And then he entered the 1st jhana, 2nd jhana all the way to 4th and then experienced the 4 formless absorptions one by one and then attained Awakening.

He did not time his sittings except taking a bit of a break when he was truly exhausted and he opened his eyes to look at the night sky to take a bit of a rest.
And like magic, right then, he Awakened.

[Similarly Zen practitioners and other "hardcore" practitioners do not time their sittings... and they tended to Awaken when they took a bit of a rest and their Buddha Nature spotaneously opened to them, their skandhas dropping away giving them a strong taste of Awakening.]

Thus, the ultimate "inorganic" method is your own physical exhaustion, your own body telling you it is time to take a break from your arduous efforts!

Nonetheless, You can use other similar methods that are "organic" and do not use digital devices: tea kettle boiling, the birds starting to chirp in the morning as you push your meditation on in the early morning, etc.

Also your question is an important question because we all need to do an electromagnetic detox! We are all heavily dependent on our devices and are sleeping, reading, and practicing in a pool of EMR. I definitely notice a huge difference when I wear my crystals than when I am not.
Many of us experienced times when we go to a garden or some greenspace, far away from wifi connections and our mind completely clears and it feels the bliss of concentration is close at hand. It is also much easier to think about one's own life and contemplate in such an environment, also due to having less electronic devices subconsciously yelling and calling us in hundreds of ways.