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Check out kasina practice. It's detailed rather thoroughly in the Visuddhimagga - which is available for free online. The jist of it is that you stare at a colored disk until the image is so familiar and habituated, it's easily cognizable by the inner eye. If it's not, then you go back to staring. Ultimately, the kasina becomes a jumping off point for the counterpoint sign and full jhana. Some people find the fire kasina easiest to practice because staring at, say, a candle produces an actual, perception after image when your eyes are closed. Rather than have to force an inner visualization, you can simply turn your mind to that inner, after-image.
What I particularly like about these practices is that you are working with the mind as an attention object almost right out of the gate. They force you to stabilize your mind quiet early. Breath perception is very effective, but I think people ultimately let their attention go a bit lax and diffuse as the breath is such an expansive object. There's really no point or place at which it occurs making one-pointedness a little harder to establish.
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So the issue with samatha meditation is that it is very hard. You either need a excellent teacher or need to be at the first level of Enlightenment.
Do cultivation instead. Bring up wholesome qualities. Loving-kindness, Compassion, Bodhicitta are some examples.
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Rather than getting bogged down in ever-changing perceptions, which can be quite nauseating, for me, this was a matter of keeping things rather simple: knowing when concentration was present, knowing when it wasn't, and knowing its qualities when it was present.
Jumping prematurely to the punchline, as this practice develops, it points the mind away from the disturbances of forms and towards the emptiness, the signless and the aimless which is where knowing, as we conventionally understand knowing, no longer happens. In short, the typical human consciousness stops dead, and yet there's still heat coming from the body, breathing continues, and motion.
Initially, however, one firstly develops a familiarity with the disturbances - sometimes called mindfullness - which can take an entire lifetime for some. This is what you're trying to describe in your question: how to reconcile with the practice of mindfulness. These disturbances are listed in various formats two of them being the 5 hindrances and the 4th and 5th fetters. If you have broken the first three fetters, these disturbances stand out like a sore thumb and are thus much easier to deal with.
To answer your question more directly: the attention is always wavering; it needs a perceptual achor to define itself as 'attention' and since all perceptions are changing, so too the attention changes. As such, the attention has various qualities, textures and scopes.
Just to throw a curve ball: there is a part of your awareness (not your six sense awareness) that doesn't have any perceptual qualities whatsoever. It doesn't move, it doesn't not move. The Buddha described it best as: "one is neither here, there nor in-between the two."