There's some input feedback missing as that is likely a temp sensor (or two) somewhere else.
But looking at it with IGN and two fans, along with my knowledge with Toyota vehicle old and new and how they do electrical logic on some things, I only suspect what I gave as being suspect control. The IGN there (yellow) would seem to be a failsafe input. When you turn on IGN does that wire got to 12v?
The module sticker helps, "yellow enable", "Blue PWM". Indicates what I had described. Yellow being a full shutoff of fans after the IGN goes to off position.
To test the Blue PWM I suspect the temp sensor needs to get hot enough to bring PWM above 0%, so the only way to test that is using a handheld scope on Blue wire while the engine starts to warm up. You could hardware a manual switch to the fans just so when it starts to warm up you can flip on the fans to prevent the overheat, then shut it down and let fans run for about a minute.
And everything after 12v in my schematic is fused somewhere. The IGN Yellow and Red+ should already be fused, but nothing stopping you from adding additional inline fuses, maybe a 0.5 or 1A for Yellow, and a 50A for Red+ (not sure what load the fans are, etc).
Just go slow and do testing where you can.