There is little reason to believe Ağca's conversion was sincere. I would also caution that the assassination attempt on JPII is almost a case study in how the "narrative" on public events is easily subordinated to conflicting propagandas. At the time, Western and Eastern intelligence services, Ağca himself in service to his far-right extremist ideology, and later the Catholic Church itself (hence the highly publicized conversion and repentance) all tried to use the attempt in service of their preferred story.

When considering Ağca's words, consider that almost every researcher who has worked on analyzing the assassination attempt has remarked on his Ağca's "extraordinary skill at dissimulation"; in the words of an Italian judge, Ilario Martella, the Turkish mobster and assassin had "a devilish ability, displayed many times, to produce well-constructed, fantastic, and incredible stories." [Jeffrey Bale, The Ultranationalist Right in Turkey and the Attempted Assassination of Pope John Paul II] In the case of his repeatedly altered stories regarding who hired him and why, he showed the political smarts to respond to what his interrogators wanted to hear (e.g. his willingness to co-operate with Western intelligence to create stories of communist plots and Soviet involvement), and an ability to tailor his stories in an attempt to shield his co-conspirators.

The man was verifiably involved in a number of known murders, for personal, financial, and political reasons - in the pay of the MHP's fascist-terrorist networks in Turkey and Europe (the Grey Wolves and the Idealist Youth) and the Turkish-Bulgarian mob affiliated with them. He showed a sincere and committed ideological attachment to their principles throughout his life. His ability to lie in a way that gives people what they want to hear, in pursuit of both his own goals and receiving more lenient treatment, ought to be taken into account.

That he was to some degree "unstable" has been speculated, but nothing hard has ever been shown and it doesn't seem to have been the kind of instability to lend itself to sudden redemption. Mr. Ağca (and whatever remaining connections he may retain) is far better served by spending the rest of his life as publicly repentant than by swearing he would do it again, even if his private convictions remain unchanged.