He wore nothing over his damaged eye – the right one. He did however have an eye shade built into his hat to protect his good eye from the sun.
He wasn't even totally blind in his right eye. His site from it was never good after a canon ball threw up grit into it at the siege of Calvi, Corsica, 1794.
The eye looked quite normal, so normal that he had difficulty convincing the Navy that there was anything wrong, thus keeping him fro invalidity pension.
Despite what people claim there is no contemporary portrait of him with a patch, and even the statue atop Nelson's Column in Trafalgar Square, London, is patchless.
He used the poor vision in his one eye to affect by claiming he couldn't see a recall order from his superior at the Battle of Copenhagen in 1801. From his position he could better see that the Danes were retreating. He is quoted as having said to his flag-captain: "You know Foley I only have one eye − I have the right to be blind sometimes".