Yes, you can use that reflector to your advantage. If you look closely, that’s probably what they used for the portrait you showed.
Another option is to use an external flash with a head that goes up and down (and might swivel); these normally have a little card in it that pulls out. This will reflect some light on your subject, but it will also give a little pop into their eyes. If you don’t happen to like the creepy ghastly look that pointing it directly at the person gives them (I don’t!), point the flash up. If you are outside, the card will put off enough brightness to give them that spot in their eyes, and the sun will still give them the backlit halo on the hair and set them apart from the background.
Another option I might try—in a pinch–would be to Photoshop the light spots in. This can look fake, and I don’t know that I’ve tried it before, but I’d experiment a bit with your dodge tool very very small.
Good luck!