A similar question came up on a Facebook group a few weeks ago, which prompted me to look into this.
In 1906, an official in the US embassy in Saint Petersburg wrote a paper on the status of Jews in the Russian Empire, which is posted on the US State Dept's website at: https://history.state.gov/historicaldocuments/frus1906p2/d409
The relevant paragraph is about 1/3 of the way down the page:
"According to the law of 1870, the number of Jews in the village councils and in the councils of municipalities must not exceed one-third of the number of the Christian members of the said council. Mayors of villages must be Christians. According to the laws of 1890 and 1892, Jews can not take part in assemblies for election beyond the Jewish pale, and the same laws forbid them to hold office under the municipalities outside the pale. Furthermore, in courts of justice, whatever the religion of the plaintiff or defendant, there must be more Christians than Jews in the jury and the foreman of the jury must be a Christian."
So, it is was not possible for a Jewish person to be mayor of a town, if Christians also lived in the town.
It is possible that the uncle held a position on the Kahal, the committee of Jewish men who oversaw the Jewish community of the town.
Lock/Lak/Lok and Kalon in Zagare/Joniskis, Lithuania
Olitsky in Alytus, Suwalki, Poland/Lithuania
Gutman/Goodman in Czestochowa, Poland
Lavine in Trenton, New Jersey and Lida/Minsk gub., Belarus