Step 1: A young woman with drooping eyelids that come and go, eye movements limited in every direction, and limb weakness that grows with exertion fits myasthenia gravis, an antibody-mediated failure of signal transmission at the neuromuscular junction.
Step 2: To confirm it quickly, the edrophonium challenge is preferred. By briefly blocking acetylcholinesterase, edrophonium boosts available acetylcholine, and an immediate but short-lived reversal of the ptosis or weakness clinches the diagnosis.
Step 3: Supporting investigations include antibodies to the acetylcholine receptor, which are almost diagnostic when present but can be negative in true disease, and slow repetitive nerve stimulation, which reveals a falling response amplitude.
Step 4: Creatine kinase and a muscle biopsy are aimed at muscle-fibre disease rather than the junction, and a routine EMG lacks the specificity of the drug test, so none of these is the single most useful choice.
\[\boxed{\text{Edrophonium test}}\]