When we aren't trying to figure out problems on transferring computer components, but when we are waking up and brushing our teeth, walking to the store, eating lunch, driving home, those are the moments were we tend to still think, when it isn't necessary.

People cite lack of necessity as the reason to abstain when their is a well understood cost to the activity—usually time or energy. I think I would find it more costly to deliberately avoid thinking than to just let my mind wonder in all the examples you gave. Additionally, if I just let my mind wonder, I might think of something cool or something I forgot to do. Actually that last sentence is downplaying the importance of idle mind wondering. I have a habit of going out for walks specifically because it fosters this contemplative state. I even make efforts to avoid people when I walk because seeing people is often very distracting so quite often I walk at night and in isolated places.

Your mind is an instrument, a tool. It is there to be used for a specific task, and when the task is completed, you lay it down

Perhaps the metaphor shouldn’t be taken so seriously but, you put down a tool because you can’t use your hand very well while holding it. My brain is stuck in my head I don’t see the benefit to turning it off, if that were even possible.

As it is, I would say about 80 to 90 percent of most people's thinking is not only repetitive and useless, but because of its dysfunctional and often negative nature, much of it is also harmful.

What Tolle seems to be describing here is a person who’s mind is filled with negative and harmful thoughts. It sounds like he is describing someone who is mentally ill. So unless that’s you, its probably not relevant.

As for useless thoughts: I once did an experiment where I tried to write down everything as I thought it. It challenged my ability to type quickly more than anything but I noticed some interesting patterns nonetheless: 90% of everything I wrote was garbage. "I wonder if..." this and "could you maybe..." that. Even though this is the case with most of the stuff we think is that a reason to stop thinking? Also I would posit that its completely OK to think about a bunch of crap. Your mind is one of the few safe places where you can produce lots of crap without worrying that anyone is going to see it and scold you for it in some way. And Edward De Bono would absolutely testify to the importance of generative thinking activities in order to get at valuable ideas even if lots of crap is made in the process.

If you infer from this that I don’t believe mindfulness you are only partially correct. I’m actually a big believer in self-awareness and particularly awareness of feelings and also in metacognition (thinking about thinking). But I aspire to a healthy diet of all types of thinking. Sometimes active focus is called for, sometimes I allow myself to daydream, sometimes I think in an emotionless critical way, sometimes I forget about what is correct and just think about how I feel or other people are feeling, sometimes I go into idea mode and become really analytical about the way I’m thinking and try to modify it to come up with different stuff. Each of these have their own advantages. An ideal might be to combine them or rapidly switch or maybe determine an optimum mixture. What people tend to do instead is habituate some more than others and consequently become better at some more than others. But the only time I think there is a problem, discussing at this level of abstraction, is when people fixate on one even when it isn’t working. Developing a habit of deliberately mixing it up is probably a good idea.

All this is assuming you want to be good at all different types of things. If you only want to be a peaceful monk then mindfulness is probably the way to go. Why does it appeal to you anyway?