Step 1: Timolol controls glaucoma by suppressing aqueous secretion at the ciliary epithelium through beta blockade, thereby cutting intraocular pressure.
Step 2: The question asks for its extra clinical edge over miotics like pilocarpine. Because it acts on secretion rather than on the iris muscle, it leaves the pupil unchanged - no miosis. That spares the patient pupillary fluctuation, drug-induced myopia and painful ciliary spasm, with simpler once or twice daily dosing.
Step 3: Reject the others - it lowers production rather than boosting outflow, it is non-selective rather than beta-1 selective, and its membrane-stabilizing activity is incidental and not the reason for preference.
\[\boxed{\text{Produces no miosis}}\]