What action should I take for a person who is insulin dependent and refuses his breakfast?

Is 63 the right age and if so why is he in a nursing home?

If you are a family member, the staff at the NH should be able to find ways to get something in him. If you r a staff member, then maybe the nutritionist can help.

Like said, maybe he doesn't like what is being served. Me, not big on eggs especially scrambled. That includes omelets. Or by breakfast do you mean everything that is served. Some people don't like a heavy breakfast. I know weird, but I cannot drink OJ, acid bothers me, and I don't drink hot coffee or tea. And if my breakfast is suppose to be hot, do not bring me a cold one especially eggs. Yes people, picky eater here. They are just going to love me in the NH my girls place me in.😊

If the age is correct, unless he has Dementia, he should understand how important it is to eat regularly to keep his sugar up.

“…..living in a nursing home….”? Why is his blood sugar management your responsibility?

Try ensure or something similar so they can just drink their breakfast.

Does he not want anything or is it that he'd prefer something different, and how is his appetite the rest of the day?

It depends what your role is. Does the person check his own blood sugar levels in the morning, or is he being helped with that?