SAMARKAND, Uzbekistan — Every five to 10 minutes, from 7 a.m. to 7 p.m. seven days a week, a fresh group of Uzbek pilgrims troops into the tomb of their late president, the dictator Islam Karimov, to pay homage at his white onyx sarcophagus, and listen to prayers chanted in his honor.

At this point, more than a year after the bejeweled memorial complex to Mr. Karimov opened, one of the few Uzbeks who has not visited is the woman who until recently was Uzbekistan’s most famous person: his eldest daughter, Gulnara Karimova, 45, who was once talked of as his heir apparent.

Ms. Karimova was also the only family member not to appear at her father’s funeral in 2016 — or at any of the more than 35,000 prayer vigils held since. In fact, since 2014, she has disappeared from public view.

Many visitors to her father’s shrine are on their second or even third pilgrimage. Schoolchildren come in groups. Newlyweds make it their first honeymoon stop, conveniently adjacent to the 15th-century Registan Square monuments, among Central Asia’s most magnificent architectural treasures.