MEXICO CITY — Drug lords in Mexico normally try to stay out of the limelight, amassing an army to help hide them and employing plastic surgeons to alter their features.

Not Servando Gómez, one of the most sought-after kingpins and a leader of a brutal gang that gave rise to vigilante groups in Michoacán State, who in recent months has made regular appearances on television, news media websites and YouTube.

In his latest online video, Mr. Gómez, known as “La Tuta,” or the teacher, is shown in a video posted this week drinking beer and chatting with the son of a former governor of Michoacán, suggesting his gang’s deep infiltration of the political class. The two men laugh and joke about several public officials.

The Mexican authorities said Wednesday that they are investigating the circumstances of the video, which was leaked to the news website Quadrantin, and will seek to question Rodrigo Vallejo, the son of the former governor, Fausto Vallejo, who stepped down in June. His resignation occurred days after a picture of his son with Mr. Gómez was leaked to newspapers.