Temporal Arteritis (Giant Cell Arteritis): This condition is a common cause of severe, intermittent headaches in the elderly, particularly those over 50 years old. The pain is often localized to one side of the head, including the temporal and parietal regions, and can be severe enough to cause significant distress. Although the classic presentation includes jaw claudication and visual disturbances, these symptoms may not always be present initially.

Tension-Type Headache: While typically bilateral, tension-type headaches can occasionally present unilaterally and might involve the scalp. The intermittent, wave-like pattern of pain could fit this diagnosis, especially if the patient is under stress or has a history of similar headaches.
Occipital Neuralgia: This condition involves the occipital nerves and can cause sharp, stabbing pains in the posterior part of the scalp. The pain can be severe and is often described as shooting or stabbing, which matches the patient's symptoms.
Trigeminal Neuralgia: Although more commonly associated with facial pain, trigeminal neuralgia can occasionally cause pain that radiates to the scalp, particularly if the ophthalmic branch is involved. The sharp, stabbing nature of the pain and its intermittent pattern are consistent with this diagnosis.

Meningitis: Although the patient does not have fever, rash, or significant erythema, meningitis can present atypically in the elderly. The severe, intermittent headache could be a symptom, and given the potential for severe consequences if missed, it must be considered.
Subarachnoid Hemorrhage: A sudden, severe headache is often described as "the worst headache" of a patient's life. While the patient's pain is intermittent and not necessarily maximal at onset, any severe headache in an elderly individual warrants consideration of this diagnosis due to its high morbidity and mortality.
Cervicogenic Headache: Referred pain from the cervical spine can cause severe, unilateral headaches. Given the potential for underlying cervical spine disease in the elderly, this diagnosis should be considered, especially if there are associated neck symptoms or limited range of motion.

SUNCT (Short-Lasting Unilateral Neuralgiform Headache Attacks with Conjunctival Injection and Tearing) or SUNA (Short-Lasting Unilateral Neuralgiform Headache Attacks with Autonomic Features): These are rare headache disorders characterized by very short-lasting but extremely painful headaches. While they typically involve autonomic features like conjunctival injection and tearing, which are not mentioned, their rare nature and potential for severe pain warrant consideration in a differential diagnosis of unusual headaches.
Neoplastic or Metastatic Disease: Although less common, tumors (either primary or metastatic) can cause localized pain due to invasion or pressure on nerves. This would be an unusual presentation but should be considered, especially if other systemic symptoms are present or if the pain does not respond to typical treatments.