When I'm painting red eyes that I want to shine, I'll paint them a base red, then the highlights will be super thin (like glaze thin) and work up to almost pink. Then add a dot of white. I also agree with
Vulcan that a darker face helps too. So I usually try to do a black wash just around the eyes/goggles before highlighting to give them that shadow.
I'm not a great painter but here's my method in practice on the grot to the right: