The most popular tactic, by far, has been not the two clocks theory , but to dispose of one of the two kinds of substance, mental or physical, and thus achieve monism. The sight of this page, and the image of it recalled after closing your eyes, would thus both be considered ideas. So, mind is real, but matter is mere appearance.
Nothing exists but ideas.
That things do seem to exist even when there is no one to observe them, and, more generally, that objectivity often seems to be successful, Berkeley attributed to ideas continuing to exist in the mind of God, even when not in that of any human. It is understandable that the more successful of the two monisms should have been materialism. According to this, matter is real, and mind, mere appearance. We might say that the mind is the functionality of the brain. The mind is what the brain does.