Q. Do you light candles next to the Matzeva when you do the unveiling?

A. Torah Lishma, (520) Nitey Gavriel (Avelus 2: 67; 3) et. al. mention that it is correct to light candles on or close to the matzeva and one should say before lighting that this is done in honour of the neshomo of the deceased quoting the name. Some matzeivos have a built in receptacle with a small door to prevent the wind from extinguishing the lights. Others bring closed metal lamps that they place close to the stone.
Horav Shlomo Miller’s Shlit’a opinion is that one should follow his tradition and the established custom of that section of the Beis Olam.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a