I do it slightly different from what has been described, and I think it is easier in the case where the section that needs the modification is small in comparison to the rest of the image, which is to use a black mask and white/transparent brush to remove the mask where needed.
To elaborate, first make the brightness/contrast layer, make changes that are much more extreme than might be required. Now the whole image is changed. Click on the clear mask in the layer to highlight it. Then take the paint bucket tool and pick black as the background color and click on the image. The mask now becomes black and image goes back to the unmodified version from below. Next with the mask still highlighted/selected, take the brush tool, adjust the opacity and flow to some low level and paint on the image section in question, with changes that can be observed in real time, until satisfied.
:Niranjan