The display really doesn't draw much power, especially not if you disable the backlight. The real power savings of display off mode comes from powering off the sensor, relaxing focus, aperture & whatever else there might be to power off in the lens/sensor assembly and signal chain.
I'm guessing timeout actuated power saving and display button actuated display off mode aren't at all different in terms of which parts of the camera are disabled, but they differ in other ways (one of the most important ones is that in display button actuated display off the sensor and the display will be automatically powered off after each shot, which will obviously not happen with power saving timeout).
If you are determined to figure out how to enter power saving or display off mode from scripts on cameras that do not have a display button, you should probably start by searching for eventprocs to enter power saving (or even display off mode -- there's a slim chance of that feature existing in the firmware even though the particular model doesn't expose that feature in menus or buttons).
Another path could be to try and override power savings timeout from its minimum settings to an even smaller delay. With incredible luck, a r/w propcase could take care of that, otherwise firmware analysis could reveal a variable or function that sets this.
