Is is better to search for the stages of insight while meditating or to allow them to arise "naturally"? Are there differences between a person who progresses through insight while looking for the different stages and someone who progresses through insight ignorant of the stages? What are the pros and cons of each approach?
Aware of stage - If you develop craving to move to the next stage this will make excessive Effort and Striving, which isn't balanced by Focus and Concentration, which will lead to Restlessness and Worry.
Unaware of stage - You might not know what is happening. Also you may not know what to do next.


So best is to balance both. Occasionally look into the stage you are, but not frequently. Perhaps once a month review would be OK.

NB: any stage of Insight Meditation happens naturally. You cannot force it. Trying to force if you will not reach the insight you are trying to achieve.