I've seen the jhana factors arise a couple of times in my practice (particularly piti and sukkha and more specifically "showering rapture / bliss / piti"). At the time they arose I refrained from pursuing, acquiring, or obtaining anything, except for mindfulness while focused on the in and out of the breath. My resolve was not where was I going or wanting to arrive, but more of an attitude of already having arrived. I cheerfully sat alone in my apartment with no expectations. In fact, I was not aware of jhana at the time and in my recent studies of jhana did I relate with what I read.
Please let me be clear: I am not speaking as though I have perfected or attained jhana. Perhaps it was "wrong jhana factors" or "right jhana factors", I don't know, but what I do know is the bliss / joy and happiness that is there far exceeds anything I've ever known. They did not come as a result of anything, they were just there... if that makes any sense.
In the end, I tend to encourage anyone meditating to remain focused on the breath, be mindful, be objective, and let come what may. I do not fret: how long and where I am going. I simply watch my thoughts, body, and primarily the breath as they arise. I watch the breath at the tip of my nose. Realize that atman and this existence is nothing, in which is not a destination, state, conceptualized notion, so it won't come by desire or ambition. Just sit and watch your conditioned thoughts arise, "note", disappear, and breathe.
Ironically I tend to believe jhana arises in the "effort" of nothing, "striving" (a contradictory and poor word) of letting the mind settle / still.
I feel as though I am deficient in my explanation, but glean what you can if you wish.