Its on the Oscillator diagram Page 7/51. The LED is used in series with a 330ohm resistor and the relay, so its failure will stop the relay operating. As the LED does have to pass a current to energise the relay its possible that the failure is just 'old age'. I would try simply replacing the LED with a modern equivalent, the only problem might be the higher efficiency of a new one
being much brighter. Any LED the correct colour that's happy passing 30 mA (the spec of the original) or more should be fine.
The cost of the LED is so low it's worth trying a simple replacement before digging too deep.
Good Luck, and please let us know how you get on.