Hyponic (night only) solely headaches are uncommon. In some ways they are distinct from migraines as the drug of choice is Indomethacin 50 mg twice daily. Neurologia. 2015 May;30(4):195-200. doi: 10.1016/j.nrl.2013.12.012. Description of series of 10 patients with hypnic headache: Discussion of the diagnostic criteria. Escudero Martínez I(1), González-Oria C(2), Bernal Sánchez-Arjona M(1), Jiménez Hernández MD(1). http://www.ncbi.nlm.nih.gov/pubmed/24953414 Standard criteria include: 
- All VAS >8
- Character – 6 patients (60%) dull and oppressive, 3 stabbing (30%), and one pulsating (10%).
- Location – bilateral in 6 cases (60%) ; hemicranial in 4 cases (40% )
- Mean duration of headache – 169 minutes (10-480)
- 70% phonophobia(noise bother) 50% photophobia (light bother)
- 2/10 trouble getting to sleep
- Onset more common during REM sleep
- dysfunction of brainstem implicated
- Suggested endogenous circadian rhythms disorder of suprachiasmatic nucleus
- loss of grey-matter seen in posterior hypothalamus in one study
- Indomethacin 50 mg bid decreased headaches by >50%
- Flunarizine, verapamil, amitriptyline, and topiramate helpful in selected cases in literature
- mentions to rule out hypertension and sleep apnea
Comment – besides sleep apnea, I have seen bruxism as a cause – unfortunately secondary to antidepressants. A bad neck can cause headaches at night and a water fill pillow (mediflow) might help. Restless legs can be a cause of sleep issues involved.