How long does a minor convert have to reject their conversion before it becomes permanent?

Question

An underage (< 12 for girls, < 13 for boys) gentile child can be converted to Judaism under certain circumstances, but they have the right to renounce this conversion upon reaching adulthood.

My question is, is there a specific time limit for renouncing this infant conversion, after which it is no longer halachically possible to accomplish? For example, suppose Shimon was converted as an infant and just turned 13 years old today. He is strongly considering renouncing his conversion and living his life as a Gentile but wants to think about it a little more first. Is it sufficient for him to make his decision by sunset? Is it too late if he makes his final decision to renounce a week after his birthday? What if he lives most of his life as a Jew and then decides to renounce his conversion on his deathbed at age 85?

• Is there a specific "hard" length of time that a new adult has to renounce his underage conversion (e.g. a hour, one day, one week, five years, etc.)?
• Is the length of time based on a "reasonable" length of time which might vary based on circumstances like how educated they are or how independent they have become from their parents?
• Is the deadline based on further life milestones? For example, a child convert might be able to renounce at any time before getting married, even if they remain unmarried for decades, but once their are married to another Jew, their conversion is permanent.

Answer 1

Tosfos in Kesubos 11A says that once he became a gadol and acted like a Jew one time, then it’s too late to reverse it

לכי גדלה - וא"ת והלא כבר גדולה היא שהיא נערה כיון שהיא בת קנס ומפרש ר"י לכי גדלה ונהגה מנהג יהודית:

The Tosfos Rid Kesubos 11A says that even if he’s younger than 13 but has the maturity of an adult then he can annul the geirus

והגדילו דר"י לאו דוקא שבאו לכלל עונשין אלא שבאו לכלל דעת ועדיין לא באו לכלל עונשין

There is a Tosfos Yeshanim that explains the way it’s done is by acting like a non Jew from before 12/13 and continuing that until after 12/13

As pointed out in the comments, R’ Moshe in Igros Moshe YD1:162 has a novel approach to the sugya and explains that a child who wasn’t told about their conversion at 12/13 can still nullify it later in adulthood when they find out.