Go to the Kelolon Village and talk to Kepilo. He's located in the southern portion of the Kelolon King area of the map. You'll recognise this area as Cooke did the Kelolon Challenge here. He will say he's got to light 10 Candlesticks or the king will take him out. The problem is they are controlled by what he calls a "Wierd Machine" and needs your help. Accept the mission.
The Candlesticks are right in front of the king surrounding the 5 Kelolon and the single human that thinks he's a Kelolon. Lighting one will light that one and the two adjacent to it. If you light one that has an adjacent Candlestick already lit, the lit one will turn off. In other words toggling a Candlestick will change the lit state (on/off) of the 3 sticks. This is the "Wierd Machine" Kepilo was talking about. After each activation of a Candlestick you will be notified of how many are left to turn on.
For reference, starting from the Kelolon Kings' left and going counter-clockwise, the first stick is "1" and on his right is "10".
The solution is as follows: 2, 5, 8, 10, 1, 2, 3, 4, 7, 2, 6, 9
The final notification screen will tell you there's "0" Candlesticks left. Talk to Kepilo again for your reward.
Simply go around and light each candlestick in order. This will have the same effect.