How to check engine temperature warning lights

[August65C10]

Hi Everybody
I'm new at this forum. First thing I would like to do is to apologize for my writing. I'm from Buenos Aires, Argentina, so english is a foreign language for me. So please forgive my mistakes.
A few days ago I purchased a 1965 Chevrolet C10 stepside with a 230 CID 6 cylinder engine.
As temperature gauge, this truck has only two lights, green for cold engine and red for too hot engine. My doubt is about how to check if the red light is working.
When I turn the ignition key clockwise to the contact position, green light lights up and so does oil and generator light, but the red light doesn't. And if I turn the ignition key all the way counter clockwise the red light lights up, but the green one does not.
My question is: Is that the way I´m suposed to check the red light? First I have to turn the ignition key all the way counter clockwise and check the red light, then turn the ignition key clockwise to the contact position and check green, oil and generator lights, and finally start the truck? Or something is not working as expected?
Many thanks in advance, your help will be much appreciated.

Augusto