The sensor is just a level switch.

.

.

it's closed when the coolant level is ok and open when it's too low.

So to light up a warning light, you'll need some form of

'NOT' circuitry.

(There are all kinds of ways of doing that we could talk about, depending on what light you want and how good your electrical skills are)

As for the expansion tank, the system wants to draw in liquid as it moves water

(that's the bernoulli effect), and the rad cap will suck in whatever it is connected to.

So if you leave the pipe from the cap vented to atmosphere, you'll suck in air every time the pump starts.

So your options are to leave the system sealed by sealing that pip form the cap, or running with a reservoir.

It makes sense for the system to have a small reservoir which is why Toyota fitted one, and explain that the system should be topped up while the engine is running and the throttle has been blipped to turn on the pump.

(If you're not using the ST205 ECU, that probably just means

"with the ignition on" for you)