Granted, the Greek term tekna has no age-related limitations. For example, we find it also in the heart-warming parable of the ‘prodigal son’, when the ‘father’ of the parable uses this term in relation to his eldest son (Luk 15:31).
However, biblically, the obligation to obey one's parents seems clearly linked with the age maturity of a son/daughter, especially when it is related to the starting of a new family. In this instance, when a son assumes upon himself the responsibility of a family (with or without children), he becomes free from his parents' authority. The same happens if a conjectural son reaches a marriageable age, and so he decides to live outside the parental home.
The passage from the parents’ responsibility for the behaviour of a son and the time in which this son assumes his own full responsibilities is well illustrated in the account of the healing of the one born blind.
We read that, in order to get the testimony of the man's astounding healing, the Jewish religious leaders called the parents of the man as witnesses.
But the Jews did not believe that he had really been blind and that he had come to see again, until they called the parents of the man who saw again, and asked them, ‘Is this your son, and do you affirm that he was born blind? If so, how is it then that he now can see?’ His parents answered, ‘We know that this is our son, and that he was born blind. But we do not know how it is that he now can see, or who it was that made his eyes to see. Ask him; he is of age; he can speak for himself.’ (John 9:18-21, Williams’ NT)
At some time previous, the parents would have spoken for (or, ‘instead of’) their son, assuming any consequences of the son's behaviour upon their shoulders; but at the time of the questioning, the man was ‘of age.’ He spoke for himself, assuming all responsibility related to his behaviour. His parents were free from exercising authority over their son.
Despite the fact that we may have some trouble fixing an exact number of years to be considered ‘of age’, the point still stands: when a son comes ‘of age’ – living outside the parental home - he becomes free from his parents’ authority.
This concept is also confirmed by the other famous parable of the prodigal son we mentioned above (Luke 15:11-32). In it we see how the father did not interfere with the decision of his son to get his share of the property. He did not oblige his son to remain in the paternal home. More likely, according to the implied background of this parable, we might imagine that the younger son informed his father not only about his desire to get part of the property but also to leave the paternal home to start a new life for himself. Moreover, the parable says nothing about the father putting a tail on his son to know in what manner he would spend the freshly received capital.
As regards women, in Biblical times they passed from their parents’ authority to the authority of their husbands (1 Cor 11:3).
Speaking about the making of a new family, Genesis 2:24 states:
Therefore shall a man leave [ozb] his father and his mother, and shall cleave unto his wife, and they shall be one flesh. (JPS)
This statement was repeated by the Lord Jesus (Mat 19:5; Mar 10:7-8), as well as the apostle Paul (Eph 5:31). In these NT passages we always find the compound Greek verb καταλειπω, from κατα (an intensive particle) + λειπω (to abandon, to leave [behind], to neglect [as in Act 6:2]). The same Greek verb was used yet by the Greek Septuagint reading of Gen 2:24.
What about the Hebrew verb used in Genesis?
Ozb has the same meaning as the Greek homologous term, plus a little more emphasis on the freedom-from-authority concept. In fact, as a derivative noun, we find that the Bible term ozub has the meaning of ‘a not-slave person’ > ‘a freedman’, as we see in Deu 32:36; 1Kin 14:10; 2 Kin 9:8.
Thus, we may safely conclude that both in Hebrew and in Greek - besides the general meaning of ‘to leave, abandon’ - we may deduce that καταλειπω/ozb both possess an authority-related idea of “to make a clean break with the authority of someone.”
Then, when Gen 2:24 speaks about ‘leaving’ father and mother, it is not merely intended that the newlyweds - from then on - will live in an independent house, but, in a more pregnant meaning, that the ‘bridegroom’ Genesis speaks about, was ready to leave behind the parental authority he was subjected to, until that moment.
So, the direct answer to your question (“Does a faithful reading of Ephesians 6:1 require adult Christian children to obey their parents?”) is: ‘No’ (excepting if one decides to remain voluntarily subjected to the authority of his father, by not abandoning the parental home).
This doesn’t mean that an adult or some who is ‘of age’ has any right to show disrespect towards his parents (and least of all, that he now has any authority over his parents). The Scriptures (1Tim 5:4) explain to us that we are obliged (as a Christian) to give compensation (or, recompense) to our living progenitors (προγονος, ‘parents’, ‘grandfathers’, and other living ancestors). The context (verses 3-16) of this passage also includes the economic care in the ‘compensation’ of these ancestors on the sons/grandchildren's part.
I agree enough with Rajesh's statement:
If your parents command you to do something that is in accord with God’s righteous standards, then to obey them is to obey God, and we are obliged to obey God no matter what age we are.
Right, but this point is applicable to every person, not only parents.
For example, a young person may also offer to more aged people some counsel derived from divine wisdom included in the Bible. In these cases, too, we may say, ‘to obey him is to obey God, and we are obliged to obey God no matter what age he is” (compare Ecclesiastes/Qoeleth 9:14-15; Job chapters 32-27).