@drubdrub - here’s what I ended up having to use on my FireHD in addition to the normal settings tweaks. It’s an app called “Keep Screen On Free” by ByOne Technology.
My settings are “Until I turn off”, “Run as a service”, “Continue keep on after screen turns off and then on”, and “Continue to keep on after Power off and then on”.
For more of my very personal “journey” ( 
) with TinyCam you can read