Shalom and thank you for your question! I am not sure where Pesach Sheni is referred to as a day of repentance, (better translated as return to G-d,) but it definitely has a strong connection to wanting to connect with G-d.
In the book of Numbers, (BaMidbar,) 9:9-13, we find that the mitzvah of the Pesach sacrifice was given, and then a group of people approached, the term is ‘came close’ to Moses and Aharon on that day and explained that they were in a state of ritual impurity and thus could not bring the Pesach sacrifice at its appointed time. They were not at all happy to leave things that way, “Why should we be discriminated against?” they complained, “by not being able to bring the sacrifice at its appointed time, amongst the rest of the children of Israel?”
Moses instructed them to wait until he consulted with G-d, and G-d told him to indeed grant them a second chance. This was not only a one-time dispensation, but covered people in future generations who would be prevented from bringing the Pesach sacrifice due to ritual impurity, or by having been on a long journey. How does this affect us today?
Pesach Sheni is a holiday! It is, according to the teachings of the sixth Lubavitcher Rebbe, Rabbi Yosef Yitzhak Shneerson, a holiday of second chances. It teaches us that if a person truly desires with all their heart, to rectify a wrong-doing, to come closer to G-d, to embark another time on a self improvement program, G-d in His mercy will provide a way.
In the times of the Temple, it was difficult to combine the circumstances of being ritually pure, with being present at the Beit haMikdash, (the Temple,) to bring the sacrifice. That is why the permission to, and possibility of, bringing the Pesach sacrifice on the 14th of Iyar was so enabling, specifically for the bringing of the sacrifice. (This did not apply to the other mitzvot associated with the Pesach sacrifice, such as eating Matzah and Maror.)
We find another instance of a second chance being given in the Torah portion of Parshat Pinchas, also in the book of BaMidbar, where we find the story of the daughters of Tzelofchad.
They were five women, named Machlah, Noa, Choglah, Milkah, and Tirzah. They had no brothers ,their father had died, and thus they were in danger of not receiving an inheritance in the land of Israel. These women however, were very righteous, and felt a strong connection to the land of Israel. They presented themselves to Moses, with a similar claim to those who wished to bring the Pesach sacrifice. Why should they not have an inheritance in the Holy Land of Israel and their family not have continuity? Again Moses consulted with G-d, and was told that the daughters of Tzelofchad would marry within their tribe, and thus receive inheritance in Israel. “Justly have the daughters of Tzelofchad spoken, you shall surely grant them inheritance amongst the brothers of their father, (their tribe,) and you shall transfer their fathers inheritance to them.” From that moment on, the laws of inheritance were changed to ensure that women who did not have brothers would inherit their share in the land of Israel.The commentaries explain that the daughters of Tzelofchad were very wise, which can be seen from the clarity with which they presented their claim. They are also considered righteous because of their eagerness to enter the land of Israel, whereas the men of the generation were hesitant, and wished to stay in the ‘cocoon’ of the supernatural protection the Jewish people experienced in the desert.
Although the only official means of celebrating Pesach Sheni today are by not saying Tachanun and by eating some Matzah, preferably Shemurah Matzah, we see that the lesson of Pesach Sheni is relevant to us today, and we can truly be happy with it. We must never lose hope that G-d will come through for us, especially when what we are trying to acheive is something G-dly!