From the Guidelines

Cerebral vasoconstriction is the primary mechanism of morning headaches in patients with chronic hyperventilation syndrome.

The reduction in cerebral blood flow through vasoconstriction is a direct result of hyperventilation, as stated in the 2018 ESC guidelines for the diagnosis and management of syncope 1.
This vasoconstriction is caused by the decrease in carbon dioxide (CO2) levels in the blood, which leads to a decrease in blood flow to the brain.
The symptoms of hyperventilation syndrome, including morning headaches, are more closely related to panic attacks than to syncope, and emotional and circulatory effects linked to hyperventilation may play a role in evoking these symptoms 1.

Patients with hyperventilation syndrome may present with symptoms such as exertional dyspnea, chest pain, and light-headedness, which may be related to unrecognized hyperventilation due to anxiety and stress 1.
Abnormal breathing patterns at rest and during exercise, as well as respiratory alkalosis, may be revealing and almost diagnostic of hyperventilation syndrome 1.

A complete and careful history and review of systems are essential for accurate interpretation and diagnosis of hyperventilation syndrome 1.
Identification of hyperventilation syndrome is important because appropriate treatment is usually successful, and addressing the underlying cause of the hyperventilation can help alleviate symptoms such as morning headaches 1.

From the Research

The mechanism of morning headaches in patients with chronic hyperventilation syndrome is not directly addressed in the provided studies.
However, study 2 suggests that headaches generated by hypoxia may be caused by cerebral vasodilation-associated stretching of the vessel nociceptors.
On the other hand, study 3 mentions that hyperventilation can lead to cerebral vasoconstriction, which may be beneficial for intracranial pressure control but can also lead to cerebral ischemia.
It is essential to note that study 4 questions the concept of hyperventilation syndrome as a scientifically valid diagnosis, which may affect the interpretation of the relationship between hyperventilation and morning headaches.

Study 5 presents a case of an older woman with hypermobile Ehlers-Danlos syndrome who experienced severe wake-up headaches due to left renal vein compression and spinal epidural venous congestion.
This study suggests that morning headaches can be caused by various factors, including anatomical issues such as nutcracker physiology with spinal epidural venous congestion.
Study 6 reviews the literature on hyperventilation syndrome and mentions that various clinical manifestations are based on the same pathogenetic mechanisms of acute or chronic respiratory disregulation resulting in hypocapnia, a rise of vascular tone, and electrolytic disorders.

Study 3 investigates the effects of prolonged hyperventilation in patients with severe head injury and finds that hyperventilation can lead to cerebral vasoconstriction and a decrease in cerebral blood flow.
However, the study also notes that the addition of the buffer tromethamine (THAM) can help sustain alkalinization in the cerebrospinal fluid and improve cerebral blood flow.