It appears that I have found it possible to focus both on the breath (as a meditation object) and to be aware of a bit of a train of thought.
Is this acceptable, or unacceptable, or should it be avoided? Or, is it perhaps simply varying "snippets" of mind-moments where I am slipping in and out of bare awareness of the meditation object?
Multi-tasking is an illusion... I have read that the mind and the senses are like a monkey sticking its head out six different windows rapidly in succession.
A great lama once told me that trying to solve a puzzle when you sit down to meditate is in actuality making another samsara.
I'd say that if you multi-task, acknowledge multi-tasking (which is at that moment on top of both breath and thoughts), let it go, and return to the breath. And see what happens in the next moment.
Perhaps when you multi-task, there is also a reason underneath that (avoiding some difficult feelings or pain, ambition to meditate "well", avoidance of boredom or tiredness) which you can become aware of (not by analyzing, just by looking), -- then acknowledge that one, let it go, and return to the anchor.
If you are aware of the snippets of mind-movements as they are alternating, acknowledge that awareness, and perhaps any induced reaction (liking, disliking, fascination, thoughts, comparison), let it go, and return to your anchor (breath).
The most important thing is that you should not be attached to your train of thoughts. Whether your CPU (brain) has an efficiency of 2 cores or 6 cores, it doesn't matter! What matters is that the cores are used efficiently. And in Vipassana meditation, they are used most efficiently when they are just shut down (unattached/equanimous to thoughts).
Such a thing as "multitasking" does not exist, since mind has only one object one time. So "multitasking" means nothing but dwelling in a fantastic illusion/construction and being totally unaware.
Calling it a puzzle is a good simile: it's just that one "solves" his own created puzzle.
People who think that they can handle more things at one time, are actually not at all aware of what they are doing (outwardly), even more so inward events.
Especially busy people, people who are proud of being "able" to handle many things at one time, hate to hear a (anti-"multitasking") doctrine like this. However, give it a honest self-proof. Record the whole stream and look at it picture by picture.
That reminds me on an essay about walking meditation, which may be of use:
...Before yogis begin practicing walking meditation, they may have thought that a step is just one movement. After meditation on that movement, they observe that there are at least four movements, and if they go deeper, they will understand that even one of these four movements consists of millions of tiny movements... The Benefits of Walking Meditation
There are times you have to think and in these cases it is fine as long as you look at the sensations through which you can understand the other aggregates.
In general meditation you have to reduce metal fabrications hence have a look at the thought, their sensation and bring the mind to an anchor. This way you can tame the verbal fabrication.
One very important step in Vippassana is to tame the fabrication. So you have to keep this in mind focused.
The idea of any Buddhist meditation is to control the mind to one and only one object of meditation, in this case vipassana.
If the mind wanders, and the meditator discovers that the mind has wandered, the meditator should go back to the meditation object immediately.
Sorry, but there should be no multitasking.
