Crossword Genius

Where people go on eating (6,3)

Ross

I believe the answer is:

dining car

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'where people' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.

'go on eating' is the wordplay.
'go' becomes 'car' (I can't justify this - if you can you should believe this answer much more).
'on' means one lot of letters go next to another.
'eating' becomes 'dining' (dining is a kind of eating).
'car' put after 'dining' is 'DINING-CAR'.

Can you help me to learn more?

(Other definitions for dining car that I've seen before include "Railway carriage with a restaurant" , "Railway coach serving food" , "meals on wheels provider" , "fast food here" , "Restaurant area on train" .)

I've seen this clue in The Irish News.
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