I approve of these shenanigans.
Twid, nicely articulated in the OP. Really, the method used to "catch" that focus doesn't really matter. But you've discovered the next portion of Mindfulness meditation.. i.e. what the hell do you do next. Personally, I find the Breath to be a key focus, as it's the one 'unconscious' reflex that we can apply conscious control over pretty consistently. I would start with a simple in-out [think "ONE"], in-out [think "TWO"]
, etc. Try to make the breathing regular. Once you get to TEN start back at ONE (the number is simply there to serve as an abstraction to focus on while you feel the effects of a long period of breath regulation while in a meditative state... otherwize, your mind will jump to the random sights and suonds around you and stay externally focused.. the counting helps refocus inwards, and we use the circular ten count to avoid "loosing the count" or subconsciously considering it a contest or something).
Sitting or lying down both work. If lying, try to breath deep into the abdomen (your stomach should rise and fall more than your chest). If you do note an internal sensation (I feel XX on my skin, I feel certain muscles tense/untense, etc), a knowledge the feeling and return to the count. Once you train the rhythm into the muscles you can drop the numbers (but most system usually replace them at this point, with a memetic to focus on, like "OM" ... yup, that's the purpose of that silly meditative device).
Once this is comfortable, the next Pranayama advice is usually to alter the length of each portion of the in-hold-out-hold breath cycle (yes, the breath cycle has 4 parts, not two). But the basics of Pranayama are what pretty much all 'eastern' meditations start from.