in the page linked in your first post, the tech spec talks about DC impedance (20℃): 550Ω±50Ω. If you have a multimeter (or decently precise resistors for a voltage divider), you can measure your device's DC impedance... and that will tell how much current the device will draw.
The minimum pulse with (and maximum frequency) on given voltage is there to guarantee proper counting / mechanical movement. If you would open the device, you would see a simple relay setup which for every close (pulse) ratchets a gear for a tooth / given angle, similar to the rotary switches used in old, pulse driven dialing / connecting systems in phone offices (see https://en.wikipedia.org/wiki/Stepping_switch).
For the referenced device of 550Ω±50Ω on 5V, it is 10mA... and 6mA on 3.3V, which is really low... (explainable by the 200:1 reduction gear for incrementing LSD by 1). Based on your forum history, I assume your Espruino device is an Espruino Pico... and a Pico can drive and sink easily 10mA. Since it has 5V compatible GPIO pins, you may run it in sink mode / open drain / open collector mode to drive it with 5V to achieve higher pulse frequency. Be aware that for sink mode the logic is reverse: pin high is idle, pin low for pulse time is for pulse.
After you have it setup, turn the coil on ('infinit' / long pulse), and measure the voltage across the coil. Should you not have sufficient voltage, you can use more than one pin in parallel for driving / sinking. I did something similar in Powering / control power of sensors / peripherals by Espruino pins. I could not use the (usually preferred) sink mode because I needed a shared ground.
Btw, I have the same DSO and I like it a lot. I 3d-printed (and painted) a case with legs for it. The legs swing out to have the DSO in an angle comfortable for reading.... (For higher frequencies I have an old, still CRT and non-S oscilloscope).
PS: You can change the title of the conversation to reflect better what this is all about.
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