Some say Tachanun on Pesach Sheni (14 Iyar); some do not; some do not say Tachanun on 14 & 15 Iyar.
What are the sources for these customs?
See related Why do we do anything for Pesach Sheini?
Those who do say Tachanun probably do so because 14 Iyar is not listed as a day where Tachanun was customarily omitted by the Tur, anyone quoted in the Beit Yosef or Bach, by the Shulchan Aruch and its Mapah, the Levush, the Eliya Rabba, the Taz, the Magen Avraham, the Beiur haGra, the Chayei Adam, the Kitzur Shulchan Aruch, the Mishna Berura and others. The Aruch haShulchan notes the custom of omitting Tachanun as foreign to Ashkenaz and deems it a 'wonder' (פלא).