Wraithwings always seemed like mysterious creatures to me... I don't feel their behaviour. Hence, my solution here was discovered by blind trial-and-error. Here it is:
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×1. Get to the checkpoint. One WW must be on the same horizontal line as Beethro, another one - on the line below. If they are not, move N and S a bit until they shift to required position.
2. Move East step by step.
3. Once Beethro get close enough, WWs will move away from him.
4. Stop moving east now.
5. Step SE, then NE.
6. Enjoy the WWs oscillating at desired positions.