This annoyance has been happening since I bought the monitor 8 months ago and any research has not turned up this specific problem. The model of my ASUS monitor specifically is the PB258Q and is hooked into my laptop with HDMI as a second monitor. Whenever my Windows 10 machine turns the screen off for idle after 10 minutes, the screen will turn blue for a few seconds "HDMI/MHL No Signal", go to black for a few seconds + power indicator flashes to yellow 'off' for a split second and goes back to white 'on', back to blue "No Signal" for a few seconds, back to black for a few seconds, and so on indefinitely until either the timer puts it into sleep mode or I move the mouse. I've tried a second HDMI cable and checked the monitor settings to be sure power saving is turned off -- "ECO Mode", and it looks to have been from the start.
The monitor does behave as expected when the machine goes into sleep mode -- blinks that blue no-signal screen once before turning off and the power light turns yellow.
I'm not sure if there is some setting that could be changed or some other way to turn off this behavior. If possible, I wouldn't mind if it blinked blue once when the screen turns off like it does in sleep mode. The continuous blinking especially in the night is even more annoying.