Crossword Genius

Cramped housing area with bad illumination at the back end of Lincoln? (4,5)


I believe the answer is:

tail light

I'm a little stuck... Click here to teach me more about this clue!

'illumination at the back end of lincoln?' is the definition.
I know nothing about this answer so I can't tell whether this works.

'cramped housing area with bad' is the wordplay.
'cramped' becomes 'tight' (I've seen this before).
'housing' indicates putting letters inside.
'area' becomes 'a' (maths abbreviation).
'with' is a charade indicator (letters next to each other).
'bad' becomes 'ill' (associated in meaning).
'tight' going around 'aill' is 'TAIL-LIGHT'.

Can you help me to learn more?

(Other definitions for tail light that I've seen before include "rear lamp" , "fitting on back of bike?" , "car shows it braking" , "followers'll see it" , "Feature of Rover, say" .)

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