Some words and phrases come from such a different culture that it it sometimes difficult to get a grip on them. 'Teenagers' for example never existed before the 20th century. At that time a culture created a new concept. Before this people were either 'children at home' or 'married and left home'. The concept of an independent person who had not left home just did not exist. There have been major sociological changes in the 20th century which would be quite unintelligible to our ancestors in flesh and in faith.
Words for 'youth' tended to be pictures of relationship rather than age. eg For of a truth against thy holy [u]child[/u] Jesus, whom thou hast anointed, both Herod, and Pontius Pilate, with the Gentiles, and the people of Israel, were gathered together,
By stretching forth thine hand to heal; and that signs and wonders may be done by the name of thy holy [u]child[/u] Jesus. (Acts 4:27,30, KJVS) The ASV 'corrects' this my using the word 'servant'; however the word is 'child' but the concept is 'servant'. In the horse-racing fraternity in the UK there is a function called 'a stable lad'. A stable 'lad' might well be ready for his retirement pension! The word started as an indicator of age but has become an indicator of relationship. The Greek word 'pais' used above is one of these.
When reading the scriptures we need be on the lookout for these words which now mean relationships. 'first born' is another which began as a biological concept but becomes a word meaning 'the heir' based on relationship rather than biological origin.
So we need to keep this kind of idea in mind when considering 'Timothy's youth'. It might indicate both/or age and relationship. The word used for Timothy is 'neotes' which derives from 'new'. This would open up a different perspective that Paul was referring not to Timothy's age but to his 'newness' perhaps referring to his role to the church at Ephesus, and the verses which follow indicate that this might be the case.
The word is used in the NT in these portionsMark 10:20 And he answered and said unto him, Master, all these have I observed from my youth.
Luke 18:21 And he said, All these have I kept from my youth up.
Acts 26:4 My manner of life from my youth, which was at the first among mine own nation at Jerusalem, know all the Jews;
1Tim. 4:12 Let no man despise thy youth; but be thou an example of the believers, in word, in conversation, in charity, in spirit, in faith, in purity. where the sense is probably from the time of their adulthood.
A similar word is one used of Paul in Acts 7:58 And cast him out of the city, and stoned him: and the witnesses laid down their clothes at a young mans feet, whose name was Saul. This is neanias "a young man," and occurs in Acts_7:58; Acts_20:9; Acts_23:17,18. My old bible college principal used to say that 'neanias' was between 26 and 40. If Paul was a member of the Sanhedrin, as seems very likely, he would have had to have been at least 30. He was probably in his mid 30s.
So the cultural pattern of the Bible was
26-40 a young man (this will be an encouragement to some!)
40-60 a man
60 onwards - an old man. Philem. 9 Yet for loves sake I rather beseech thee, being such an one as Paul the aged, and now also a prisoner of Jesus Christ.
Folks like Greg would not be at the starting line yet! :-D
Hope this gives you some ideas...
Ron - the aged! :-D