The iris of the eye cannot react fast enough to the a flash. So whatever amount of iris is showing is whatever amount you can see when you are ready to take the shot.
If there isn't enough iris you can fix it in post (as has been done forever, back in the 80's this was done with mcdonald tooth lacquers and colored pencils). Or you can increase the ambient light until the iris gets smaller - i.e. brighter modeling lights. or just some brightness to the room. An obvious challenge there is too much light and it can affect the exposure. Most film portrait photographers used medium or large format cameras with iris shutters so this wasn't an issue, now with most cameras being Focal plane, you have to pay a little more attention to it.
Lighting angle is about creating depth on the face, so that's what determines the angle of the light. However, this will normally illuminate the eyes appropriately to get the iris to close down if the modeling lights are bright enough.. To get good dimension with portrait lighting you will normally see a bright catchlight from the key light around the 11 or 1 o'clock position (depends on which side you position the key light). If you cannot see a decent catchlight in both eyes, you probably also won't get a nice sculpting shadow on the face.
Unfortunately sometimes with some people, it takes more light or they are more sensitive to light so you get them squinting.