You can get digital turns counters which just need an AA cell for power. Each turn is triggered by a 'proximity switch'.
Basically, you attached the supplied small neodymium magnet to the shaft of your winder, and position the sensor about 5mm away, and each rev will trigger the counter.
All very simple.
Here's an example:
https://www.ebay.co.uk/itm/5-Digit-C...-/324311172604
You can make a counter using a cheap pocket calculator, which I did some years ago on a hand wave-winder but it's a bit of a faff. (See pic below).
Basically, it involves connecting a microswitch across the equals sign contacts on the calculator PCB, and to fit a cam on the shaft of the coil winder so that with each rev, the microswitch shorts out the 'equals' button of the calculator. To start counting, you press '1' then + +, then each time the = button is pressed (or shorted out) it will increment by 1. (Just need to make sure it's not an auto turn off calculator because if you don't note the turns right away, the calculator will shut off!).
Lots of videos on using calculators as turns counters on youtube.
You can use a reed relay rather than a microswitch, and trigger it with a magnet of the oil winder shaft. EG:
https://www.youtube.com/watch?v=L1FP2NIWj6k
Hope that's of interest.