Hopefully this might help, with you going along the Arduino route.
It's my 555-A-Like circuit, developed for something else but maybe it could be useful for this.
https://www.youtube.com/watch?v=_Fh3G0Nk8xYIt features a 128x64 OLED screen (cheap and effective at approx $3.50) and 2 pots for Frequency and Duty Cycle.
It doesn't need the screen and will run without it.
1% to 95% duty, but at the moment only 1Hz to 12Hz because of the screen routine. I'm going to speed the thing up for 40Hz. Anyway, will add the code link to the vid description and the Fritzing breadboard circuit is below,
The thing being, that small adjustments in duty cycle might be part of this slight flicker situation too. A 60% duty cycle would flicker less than 50%, but in the description of how their system works Picower could still say it was on for half the time, off for half the time. If the optimal was 54%, that could easily be set too. Once all was known, set up and working, the pots could be removed and either resistors put in place or the code redone.
An Arduino's outputs can deliver 40mA, more than capable of driving a transistor...which means overcurrent will be no issue. Run anything via the transistor instead. 1K resistor from the output pin to the Base, Emitter to ground, Collector out to the load.
My wife's Dad passed away last November due to this and her mom is showing signs of a similar path. All of us might end up with the damn condition, so this research can be self centered for the future as well as helping those who have it now.
The glasses idea was marvellous ! which brings thoughts of a sleep cap for overnights.
Wasn't there something about flickering ping pong balls on the eyes at nights recently ?
Best wishes to you, your father and family Jim