I find this somewhat confusing. Can you explain why someone would do something without having a purpose for doing that thing? In other words, if there is no motivation for doing something, then what would compel someone to do it?
You meditate when you feel a meditation coming on, rather than try to induce meditation. If you try to induce a meditation, you will always have a purpose to meditation. The purpose or motive will then guide or shape the meditation.
But if you meditate when you feel a meditation coming on, then you have a chance of something as purposeless as idly and without point or purpose watching the sunlight dapple your lawn, the breeze wave a field of grass, or the flies buzzing fresh dog poop.
On the other hand, if you find you have a purpose, then you don't try to shake if off, but you just recognize it, and if possible, without judging it.
None of the above should be taken to mean I don't sometimes discover that I am trying to meditate towards an end. Since some of my meditations in the past have been either quite pleasant or quite revealing, I tend nowadays to feel a meditation coming on, and then a desire to have, once again, a pleasant or revealing meditation. But that desire can get in the way of genuine meditation. At least, what I consider genuine meditation -- which is, of course, meditation on MysticSangha's tush.