Final answer:
The correct client statement indicating understanding of timolol eye drops administration for glaucoma is looking up while applying the drops to avoid contamination and ensure effectiveness. Rubbing the eyes or closing them tightly should be avoided to prevent increasing intraocular pressure.
Step-by-step explanation:
The client who has a new prescription for timolol eye drops to treat glaucoma demonstrates an understanding of how to correctly administer the medication with the statement: "I will look up when putting the medication into my eyes." This technique allows the eye drops to be accurately placed without contaminating the dropper and ensures the medication is applied where it can be most effective. The client should avoid rubbing their eyes, which could distribute the medication away from the intended area, and should not clean their eyes inward as this could introduce contaminants. Closing the eyes tightly could increase intraocular pressure, which is counterproductive in the treatment of glaucoma.