The Pi Zero has one LED, led0 (labeled 'ACT' on the board). The LED drive is 'inverted' so, when it defaults to 'brightness 0' this turns the LED 'on' !
The system software issues a 'trggger' that sets 'brightness 1' (for a short time) during 'disk activity' (i..e during SDHC card access) which turns the LED off.

Needles to say, when running from batteries, wasting XmA on an almost permanently 'on' LED is a luxury we can't afford :-)

You can control, the LED from a CLI / script by removing the 'disk activity' trigger and then 'manually' turning it on/off as follows :-

# Set the Pi Zero ACT LED trigger to 'none'.
echo none | sudo tee /sys/class/leds/led0/trigger

# Turn off the Pi Zero ACT LED.
echo 1 | sudo tee /sys/class/leds/led0/brightness

# Turn on the Pi Zero ACT LED.
echo 0 | sudo tee /sys/class/leds/led0/brightness


To permanently disable the LED, add the following lines to your Pi's /boot/config.txt file and reboot:

# Disable the ACT LED on the Pi Zero.
dtparam=act_led_trigger=none
dtparam=act_led_activelow=on