The "perfect grilled cheese" will mean something different to just about everyone. It is about the type of bread used, the selection of cheese (s), butter on the outside, fry pan vs. iron skillet. Lots of choices to be had.
One common thing, if I could be so bold, is that the cheese needs to be warm and gooey and melted. The sandwich CAN not be cold on the inside and black on the outside from having heat to high.
In resent years, I like to get the iron skillet going at about 4 (electric stove, no clue what that equates other than not quite medium heat), then get the sandwich ready. To encourage the sandwich to heat all the way through, I will take an 8" x 8" cake pan and flip it over the sandwich. This keeps the heat in and doesn't smush the sandwich like a panine press would. It also always for a slower browning of the bread and allows for the heat to go all the way through the sandwich. Remove the pan, flip the sandwich, and put the pan back on. I can get a lightly browned grilled cheese sandwich that has gooey cheese on the inside every time doing this!