Hi!
The Zero Lipo is oscillating between on/off: When the Zero Lipo starts drawing current, the input voltage drops below the undervoltage shutdown level and the Zero Lipo shuts down. When it shuts down and stops drawing current, the input voltage rises again, and the Zero Lipo will start again. This fast on/off oscillation is what you hear as the high-pitched noise.
The voltage drop at the input is most likely caused by the resistance of the battery wiring you’re using, give it a try using shorter and/or thicker wiring. If that doesn’t help, check out the battery too, many of the batteries on eBay don’t live up to the advertised spec, as was the case here for example: RPi3 plus Zero Lipo not powering up