Were there beacons on both sides of the White mountains and if so were they both lit?

Question

In The Return of the King, the beacons of Gondor were placed on the north side of the White Mountains, so they could warn the people of Anórien of danger. However, the regions south of the Mountains were far more populated than the north. Since it is far more populated it would be able to muster a much greater army than the north. So my question is, would it have made more sense if the beacons were placed on the south side of the mountains? Why were they placed on the North side? and if they were beacons on the south side where they lit?

Answer 1

Beacons were located on the North and South and it is most likely they were both lit.

As is stated in Wad Chaber's extensive answer, there were beacons to both the North and the South.

“Gandalf telling him of the customs of Gondor, and how the Lord of the City had beacons built on the tops of outlying hills along both borders of the great range”
_{Return of the King: Book 5 - Chapter 1, Minas Tirith}

Gandalf then suggests that the beacons of the North were lit, although he can not see to the other side of the White Mountains.

“It is long since the beacons of the North were lit,’ he said; ‘and in the ancient days of Gondor they were not needed, for they had the Seven Stones.’ Pippin stirred uneasily.”
_ibid.

Some soldiers speculate the reason for lighting the beacons was because of the Umbar coming from the South. We, however, (film wise) know it was Merry's Pippin's doing, and in that case it seems likely that both sets of beacons were lit. As the one fire in Minas Tirith would've been seen by both the North and the South beacons. However in the books the beacons were lit before Pippin reached Gondor (thanks @Teem Porary), but it is still most likely that both sets of beacons light from one central beacon in Minas Tirith.

“There is a great fleet drawing near to the mouths of Anduin, manned by the corsairs of Umbar in the South. They have long ceased to fear the might of Gondor, and they have allied them with the Enemy, and now make a heavy stroke in his cause. For this attack will draw off much of the help that we looked to have from Lebennin and Belfalas, where folk are hardy and numerous. All the more do our thoughts go north to Rohan; and the more glad are we for these tidings of victory that you bring.”
_ibid.

If there were however two ways of setting off the two beacons, it is possible from the above that they did not send for help from Lebennin or Belfalas as they were already under attack. Since all our point of view characters are North of the hills, we can only guess that the ones on the south were lit.