Does Ecclesiastes give an example of a time to tear and a time to mend?

There are various ways of tackling the book of Ecclesiastes, with the example you give being a method I had never considered before; taking “chapter 3 as a sort of index into the rest of the book.” I know and appreciate the worth of taking an entire book of the Bible as needing to be read within its own context, detecting the writer’s style and paying attention to his repetitions, but that the rest of the Bible may also speak to the matter, giving further insights (either before that particular book was written, or after). I had never thought to examine chapter three’s 14 pairs of opposites, expecting to find additional reference to tearing (vs. 7) within Ecclesiastes.

Upon examination, the 14 couplets cover every range of human activity, beginning with life and death (vs. 2). Then come three creative and destructive activities (vss. 2-3) followed by human emotions both public and private (vs. 4). A move is made to friendship and enmity. Apparently, in that era, stones refer to filling up your neighbour’s field with stones or gathering the stones they throw and using them to build something), and a time to say hello and a time to say goodbye (vs. 5). The next two have to do with possessions and our resolutions concerning them (vs. 6). Finally, a return is made to the various creative and destructive activities of man (vss. 7-8). The key point in all such affairs is the element of time – seasons – life’s rhythms. Ignore that and you suffer burn-out. But if we place our times in God’s hands, we will find balance and, at the end, God’s purpose which is detailed in the last chapter.

You referred to 1 Kings 11:10-13 as a possible connection. However, I do not know if God warned Solomon of tearing the kingdom away once it had been given to his son prior to Solomon collating all those wise sayings.

It seems likely that his collection was a life-time’s work with formation into a structured book happening after much consideration. Given how Solomon states the conclusion of the whole matter of the vanity of life in its last chapter 12, showing that it has purpose in obediently fearing God, who alone can break through the brassy heavens above us, I’ve viewed his last chapter as key to unlocking all that went before. And it speaks of the ultimate physical rending: the breakdown of the ageing body as death gets a grip as in 12:6-7:

“Or ever the silver cord be loosed, or the golden bowl be broken, or the pitcher be broken at the fountain, or the wheel broken at the cistern. Then shall the dust return to the earth as it was, and the spirit shall return unto God who gave it.”

That is why 12:5 speaks of the mourners going about the streets. Old age and impending death have a way of focusing our minds, to expose vain thoughts and to seek God’s mind on matters to heal all the damage of a merely physical life. Back to 3:7. One translation says, "A time to rend, and a time to sew". [Y.L.T.] Rending was a term used in the Bible for showing great grief, when garments would be torn and sack-cloth worn instead, and ashes placed on the head. But the writer of Ecclesiastes, a rich powerful ruler, would never be engaged in sewing (repairing) such rent garments! However, he would be very involved in the showing of grief at times of mourning. Indeed, there would be times of national crisis when he would be expected to lead the nation in public demonstration of rending his fine clothes, to then wear sack-cloth and ashes.

That is why I think chapter 12 is a fitting link to 3:7. The whole chapter points to impending death, and when that time inevitably comes, it would be better for young people reading his wise sayings to have taken to heart its counsel, and to have sought God early. Only those who do that will no longer find the heavens as brass, “under the sun”, but know the satisfaction of living to honour God, before it comes time to die.