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How's this for a sad, haunting image of what old age is like? The phrase "thine own deep-sunken eyes" is meant to stand for the opposite of everything that is beautiful about the young man, and to paint a scary picture of what he will become.
Line 7: In this moment, we can see those eyes sinking back in the old man's head until he almost looks like a skull. The speaker of the poem wants to remind us that death is always waiting for us, so there's no sense in wasting time.