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Is there a glove box light on a 2005 Honda Civic LX? I don't have one working now and didn't realize whether it is supposed to have one or not.

 
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No, I do not believe there is. Not on 2003 EX at least. The easiest way to know is to look and feel for a bulb!

 
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definitely isn't one. Only major changes between years had to do with the facelift/rear bumper, rear tail lights, and and the DS O2 sensor (between 03 and 04), and some center console and instrument cluster redesigning (between 02 and 03, IIRC). You can make one, though, using an LED strip and a NC momentary switch

 
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not a helpful DIY article, rather a question, so moved out of DIY section

 
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here's a quick circuit schematic (yes, it's really this simple)



Just position the momentary switch such that the glove box door pushes the momentary switch, opening the circuit. This is, more-or-less, the circuitry behind the "door" setting on your map lights, except no resistor, since incandescent bulbs don't require them.