From Halopedia, the Halo wiki
To see the affected Jackal, play through the level normally until you are past the alleyway, otherwise known as "Sniper alley", with the Drones. Proceed to the next alley, go through a bit, stop, and turn left and you should see a Jackal Sniper. Do not kill him. Go trigger a checkpoint. Go back to the Jackal, and you should see him fall over and die by himself. It only works when you are both aware of each others' presence, similar to enabling a cheat in Halo: Developer mode.
Also, randomly, you can see a Jackal Sniper kill himself on the level Regret. This Jackal Sniper will appear where the turrets are, right after the gondola. The Jackal will run, drift, and fall to the lake.