Reading narrowly is about making sure that the point of view you've tentatively committed to is a valid one. It means you have to search for texts that detail some of the sub-issues that you identified as being part of the big picture. To find these more detailed texts, you'll find that the bibliography in the introductory text you read will be a good start. It will point to:

texts that are dependable (their appearance inside a standard introductory text will suggest their dependability)
more detailed texts on the specific topic
texts that relate to the points you still have to research and
writers in the field who are valued.

Remember that you will need to put your efficient reading, critical reading and note-making strategies into practice as you carry out this narrow reading.