Shalom and thank you for your question!
We light a Yahrtzeit candle for Yom Kippur, using it at the end of Yom Kippur to light the candle for the Havdalah ceremony that marks the end of Yom Kippur.
There is also a custom to bring a Yahrtzeit candle to the synagogue on Yom Kippur, which is called a Ner Chaim, a candle of life. Those who have deceased parents also light a Yahrtzeit candle for them at home.
To the best of my knowledge we have no obligation to light a Yahrtzeit candle for Rosh Hashanah.
It is however practical to light one for the following reason.
On Yomtov, that means a Jewish festival that is not the Sabbath, it is permissible to warm up food that is to be eaten on the festival, and even to cook or barbecue the food if it will be tastier when prepared on the festival. To warm up the food or cook it, one cannot turn on electricity or light fire. In places where people use gas stoves, they may be lit from a pre-existing flame, meaning a flame that was lit before the advent of the festival. If candle-lighting for example for the first night of Rosh HaShanah was at 6.35, the flame had to be lit before that. There are 48 hour candles, so that if there is a need for fire during Yomtov, it can be transferred from the 48 hour Yahrtzeit candle using a match, in order to light a stove, barbecue, or cigarette. (Some people smoke on Yomtov and others refrain.) Once a fire has been lit on Yomtov from a pre-existing flame, it can not be put out. If the stove was turned on, the flame may be turned higher but not lower. If a backyard grill was lit, from a pre-existing flame, (with coals, not electric,) it cannot be put out. It must be allowed to die out by outself. (In a safe manner.)
Due to the above, it can be useful to have a candle burning in a safe place on Yomtov.
Sorry this answer didn’t reach you before Rosh HaShanah, but the information is relevant to the upcoming festival of Sukkot…
Outside of Israel, the final day of Sukkot is Shmini Atzeret, and the day after that is Simchat Torah. This means that you have two days of Yomtov, in which case the information about lighting fires is as mentioned above. On a one day Yomtov, a 24 hour candle is sufficient.
We hope you find this information useful and wish you a good sweet year, in good health and happiness!
