He must be one who manages his own household well, keeping his children under control with all dignity (but if a man does not know how to manage his own household, how will he take care of the church of God?), …
1 Timothy 3:4–5

…namely, if any man is above reproach, the husband of one wife, having children who believe, not accused of dissipation or rebellion.
Titus 1:6 (emphases mine)

One of the indications that a man is qualified to be an elder is the leadership he demonstrates in the context of his family. A man who is failing in leadership in the home is not qualified to serve as an elder in the church.

The indications that he is managing well in the home are both negative and positive.

His children must be under control with all dignity. As a father, a man is not to be the despot of his home. He is to manage in a way that reflects servant leadership. His commitment to leadership in the home is serious, yet respectful. Loving leadership from the father and biblical submission by the children must characterize the home.

In Titus it states that he must have children who believe. It has been debated whether this means that the children of elders must have come to know Christ as Savior. This seems unlikely for numerous reasons, not the least of which is the fact that no person has the capacity to make their children become believers. That is God’s work alone. But we do have the responsibility to teach our children to be faithful. As we teach our children to be faithful, we pray God will draw our children to Himself.

In Titus, it is further emphasized that they should not be accused of dissipation or rebellion. If children are faithful, they will not be accused of living lives that are careless and reckless. Nor will they be defiant towards authority or intensely disobedient.

When it comes to the church, Paul reminds us that the elders who “rule well,” the same word as “manage,” are to be considered worthy of double honor. This is specifically because they work hard at preaching and teaching.

The elders who rule well are to be considered worthy of double honor, especially those who work hard at preaching and teaching.
1 Timothy 5:17

Such leadership begins in the home. If a man demonstrates biblical leadership in the home, he may be qualified to become an elder in the church.