Are you putting a light cover over their cage at night? This will help them to feel secure and safe (keep using the night light as well so they can see and move around their cage safely). Budgies are prey animals so if you are staring into their eyes, they won't relax and go to sleep. They'll watch you to make sure you're not going to do anything to hurt them. Budgies need roughly 10-12 hours of sleep a night as well as their naps through the day. They like to sleep on swings and perches that are up high, so arrange their cage with a good variety of sleeping position options. I'm pretty sure your boys will be getting enough sleep. I think they're just waiting for you to move away before closing their eyes and dozing off.
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