Blepharitis: Given the patient's history of dry eyes and symptoms of bilateral eye redness, occasional itching, and thin clear drainage, blepharitis is a likely diagnosis. It is a common condition in geriatric patients, especially those with a history of dry eyes.

Dry Eye Syndrome: The patient's history of dry eyes and current symptoms of eye redness and itching could be exacerbating their dry eye condition.
Allergic Conjunctivitis: The occasional itching sensation and clear drainage could be indicative of an allergic reaction, although this is less likely given the patient's age and the absence of other allergic symptoms.
Conjunctivitis (Viral or Bacterial): The symptoms of eye redness and clear drainage could be indicative of a viral or bacterial conjunctivitis, which is common in institutional settings like SNFs.

Acute Angle-Closure Glaucoma: Although less likely, this condition is a medical emergency that requires immediate attention. Symptoms can include eye redness, pain, and blurred vision, but the absence of pain and vision changes in this patient makes it less likely.
Endophthalmitis: This is a rare but serious infection of the inner eye that can occur in patients with a history of eye surgery or trauma. It is a "do not miss" diagnosis due to its potential for severe vision loss.
Keratitis: An infection or inflammation of the cornea that can cause eye redness, pain, and vision changes. It is less likely in this patient but should be considered, especially if there is a history of trauma or contact lens use.

Sjögren's Syndrome: An autoimmune disorder that can cause dry eyes and other systemic symptoms. While possible, it is less likely given the patient's age and the absence of other systemic symptoms.
Trachoma: A rare infectious disease caused by Chlamydia trachomatis that can cause eye redness, itching, and discharge. It is unlikely in this patient given the lack of exposure history and the presence of other more likely diagnoses.