Lets play name that connector!

[viperidae]

This is the radio from a 2005 Honda Accord.
It's 20 pin, contacts on top and bottom.
The increments on the ruler are 0.5mm. It's 9.8mm wide, 4.75mm high, and 4.15mm deep.
The depth of the hole is 2.15mm.
Pin pitch looks to be about 0.78mm, or 0.030"

[HwAoRrDk]

Are there any markings on the connector? They can usually be used to identify the manufacturer, which can give a good start to identifying the exact part. Markings may not necessarily be textual, just a logo. For example, the Japanese company Yazaki use a simple, easily-missed arrow shape.

Also, knowing the OEM (i.e. not necessarily Honda themselves) of the radio itself can give a clue to likely connector manufacturer. If an Asian company, look at Asian connector manufacturers, and so on for European, American, etc.

Also bear in mind that for a product more than a decade old, the manufacturer may have discontinued the part, so will not appear in current catalogues.

[viperidae]

I'm not sure who makes the radio

It's quite possibly Alpine

Looks kinda like this style
http://www.townes.com.tw/product_detail/land-ctop-2/index.php?Product_SN=216307&PHPSESSID=&Company_SN=17325&Product_Site_Classify_SN=12173

I couldn't see any markings on it at all

Update: I may have found a winner winner, chicken dinner.
http://www.wconconnector.com/sale-9429747-elevator-male-straight-headers-0-8mm-pitch-smt-pcb-to-pcb-connector.html
Now... where to buy these from in less than 1,000qty

[viperidae]

... or one of these... https://www.molex.com/pdm_docs/sd/533091070_sd.pdf

[HwAoRrDk]

I'd say you're on to a winner there with that Molex part. Being a Molex Japan part also goes with it being in a product from a Japanese auto manufacturer. It doesn't happen to have an 'MXJ' marking anywhere on it, does it? That would confirm it.

[viperidae]

There may actually be something on the back of the connector. It's a pain to keep pulling the thing out the car though and I can't make it out on the picture

[pcmad]

these connectors are found in small eletronics like digi cameras but dot know what they are called