An eyecup is called an eyebath in Britain.    From Wordnet, Princeton University. 

If her answers are right, we postpone the eyebath.    From Wordnik.com.  [Exodus From The Long Sun]

'These units can be fitted with an internal eyebath, optional alarms and lighting.    From Wordnik.com.  [Processingtalk - processing industry news] Reference

Director URL: radarmusicvideos.com/users/eyebath.    From Wordnik.com.  [The Lost Levels 'The Early Sheets' on Vimeo] Reference