Ok, I understand. Most likely, the camera has a MOSFET or NPN transistor switch to ground, and the Flash has an input where the pull-up resistor is returned to an internal voltage which is much higher than the camera's internal voltage.
With the flash unit turned on, but not connected to the camera, what is the voltage at the trigger input measured with respect to the flash's ground pin? Is it 8 to 12V?
Put your meter in the DC current measurement mode, ~100mA scale. With the flash powered, connect the red probe to the flash's trigger input, and the black probe to the flash's ground pin. That should fire the flash, but I want you to measure the peak current while the probes are in place, just as the flash goes off.
What is the camera's battery voltage?