Source of illumination, bad in the morning in work (3,4)
I believe the answer is:
oil lamp
'source of illumination' is the definition.
(oil lamp is a kind of source of illumination)
'bad in the morning in work' is the wordplay.
'bad' becomes 'ill' ('ill' can be similar in meaning to 'bad').
'in the morning' becomes 'am'.
'in' indicates putting letters inside.
'work' becomes 'op' (abbreviation for opus).
'ill'+'am'='illam'
'illam' put inside 'op' is 'OIL LAMP'.
(Other definitions for oil lamp that I've seen before include "Early means of illumination" , "Light that burns kerosene" .)