Final answer:
The next test that should be performed is a blood test to measure the level of cobalamin (vitamin B12). Cobalamin deficiency can lead to various neurological symptoms like those experienced by the patient, making it a probable underlying cause of his condition.
Step-by-step explanation:
In the case of a 66-year-old man experiencing tingling sensations, clumsiness, gait difficulties, weakness, depression, irritability, and decreased reflexes, the appropriate next step would be a blood test to measure the level of cobalamin (vitamin B12).
The symptoms described could potentially be indicative of a cobalamin deficiency, which can lead to neurological problems such as peripheral neuropathy and subacute combined degeneration of the spinal cord.
A deficiency in cobalamin can result in impaired production of myelin, which insulates nerve fibers, and can lead to the varied neurological symptoms the patient is experiencing.
A neurological examination, as described in the provided material, can help pinpoint areas affected by possible nerve damage but does not replace the need for blood tests to confirm nutritional deficiencies.
While other tests could be useful depending on additional clinical symptoms and history (such as glucose levels for diabetes, TSH for thyroid function, or neuroimaging for structural abnormalities), the clinical scenario presented points towards a need to first rule out cobalamin deficiency before considering other less likely possibilities.