Blink eyes constantly can be good for our eyes. It can keep our eyes clean and moist so that the eyes can focus properly. But I never heard that people can blink eyes when the eyes are closed. For your situation, you must be very tired that cause the blink eyes when you try to close eyes for a nap. Or you are so exciting that can't fall asleep. Don't worry, it is not a big problem. Keep calm, and take a deep breath, then, try to relax, yourself, everything will be OK.
This is a normal physiological phenomenon that the eyes will still blink when people are having a rest and their eyes are closed. This is because that no matter when people are having a snap or sleeping, some organs of the human body are still in the operation, that is why people will still blink, just as people will sometimes grind their teech they are sleeping. As long as the blinking is only once in a while, it is a normal phenomenon, but if you blink frequently when you are sleeping and it has affected your sleep quality, you had better go to the doctor's for an examination to see it there is any eye problems.
Well, generally speaking, blinking can be kind of normal for people. But on the other hand, if someone like you suffers from unmoral blinking, we can say that is an eye problem. Generally speaking, some blinking occurs when the eye is exposed to an irritant, such as a spec of dust. Also, according to some researches, a healthy individual who blinks excessively may be responding to a side effect of a medication especially a stimulant. And besides, psychological discomfort or even an allergy can just cause it too. So for your situation, I have to say that it can be caused by some allergies. So anyway, just find the real reasons.