Translation:But it is necessary to take the time to search.
Various interpretations can be valid here, since this sentence is out of context and the beginning of the story is missing.
Let's imagine a start to this story to clarify various possible translations:
- Elle ne trouve pas ses gants. Mais il faut prendre le temps de chercher et elle est pressée. (she can't find her gloves. But she should take the time to search and she is in a hurry).
Now, change "elle" to "je", "il", "nous", "vous", "ils" or "elles" and the "il faut prendre le temps de chercher will also change to I, he, we/on, you, they... accordingly.
"Il faut" never points to a real person. This is an impersonal construction literally meaning "it is necessary to".
- "il faut prendre le temps de chercher" = it is necessary that (we, you, anybody, all of us) take the time to search = We/You/One has to take the time to search.
- "il faut que je parte" = it is necessary that I go = I have to go / I need to go / I must go.
It's kind of like the use of impersonal constructions using "on" as a subject. At the most literal level it is, "It is necessary to take the time to search," but depending on context you could also correctly translate it as "We must take the time to search" and "You must take the time to search."
In the idiomatic expression "il faut", "il" is not a person. It is an impersonal expression meaning "it is necessary that" or "it is needed that".
Without context for this sentence, in particular to whom this is adressed, you could translate "we need to..." or "you need to..." or even (talking about a third party): "he/she needs to..."
Maybe this example will help. Imagine a history professor lecturing on artwork stolen by the Nazis and presumed lost for decades. She might conclude by saying, "We must take the time to look." She does not mean that she and the students should mount an expedition and search for the art. She means that WE, humanity, should keep up the search. She means WE in the impersonal sense.
No. You would need to include the object if you include "for". For what? In this sentence we would know what they are searching for from context. But it could also be added here, with for, if we did know what it was. It depends on the context... "I can't find my watch, and I am already late! But it is necessary to take the time to search." OR "I am running late for my appointment! But it is necessary to take the time to search for my watch."