given this reference text about 1891 Cypriot legislative election, What caused the non-Muslim seats to drop in 1886 to 10,030?
The Legislative Council consisted of six official members appointed by the High Commissioner and twelve elected members, three of which were Muslims and nine of which were non-Muslims.

The island was divided into three constituencies, each formed of two districts. Each constituency elected one Muslim and three non-Muslims. Muslim voters had one vote, whilst non-Muslims could vote for up to three candidates. Due to the high levels of illiteracy, voting was not secret, with voters required to tell the polling officers their candidates of choice, often in front of agents of the candidates.

Suffrage was limited to men aged over 21 who had been permanent residents during the five years prior to the elections, and who had paid either the verghi tax (which was levied as an annual payment of one four-thousandth of a property's value, 4% of rental income or 3% on profits or salaries) or rent for a dwelling or shop within the last year. However, of the estimated 40,000 taxpayers in the territory at the time of the elections, only those that had been able to pay their taxes on time were able to register to vote. The number of registered voters for the non-Muslim seats dropped from 15,408 in 1886 to 10,030.
user
Due to the requirement of paying your taxes on time in the previous year to be able to register to vote, the number of voters that were non-Muslim dropped.
assistant