Kicking RJ11 cash drawer via PC's serial port
It does require more voltage. This PDF gives a schematic, albeit for a different model but also using RJ11:



It requires 24V for a few hundred ms, at least 1A.

See also this Epson control PDF. That has the solenoid on pins 4/5, which I think is more common than 2/3.

You should be able to find the solenoid by identifying the pair of pins with a small non-zero resistance. You don't "apply voltage then cut it", you need to supply a pulse through a transistor or suchlike. You could probably control the transistor through DTR.