Tim Drake was about 13 years old when he deduced Batman’s identity and stepped into the Robin role, which is the version of the story most sources point to. That means he was still a young teen when he helped bring the situation around after Bruce’s absence and Dick Grayson had taken on the Batman mantle.

What happened

  • Tim first figured out that Bruce Wayne was Batman after studying the earlier Robin era and the Batman family dynamic.
  • In the A Lonely Place of Dying storyline, he pushed for Batman to return after the crisis that had left the mantle with Dick Grayson.
  • The commonly cited age for Tim at that point is 13.

Small clarification

Your wording mixes a few Batman story beats together, but the core answer is still the same: Tim was around 13 when he became Robin and got involved in bringing Batman back into the fold.

TL;DR

Tim Drake was about 13 years old when he found out Batman’s identity and became part of the chain of events that led Bruce Wayne back into the Batman role.