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Is there anything straightforward about this VHS capture?

I bought a Hauppauge HD PVR2 and it came with this cable. It has an 8-pin DIN on one end, and five RCAs on the other, giving this arrangement:

Bk1 – audio
Bk2 – audio
Blue – Component
Red – Component
Green – Component

Being brand new to VCR capture, I had assumed that good-quality VCRs had component output, but I soon learned that was not the case, so the cable was of no use to me. But I could use it to capture Composite video via the blue plug, I think it was.

So I tried to buy the special cable required, from Hauppauge USA; 8-pin DIN one end, 4-Pin DIN and 3 RCAs the other. "No, we don't sell to Australia", when I tried to checkout.
Tried Hauppauge Singapore, the closest office. "Mr Burns, please contact Hauppauge UK"
Tried Hauppauge UK. "Guy, you can buy this cable from our US website. Here is the link"

Back to the USA website, grabbed a screen shot, emailed it to the UK, and after they looked into it, they convinced Singapore to sell me a cable.

Great. Cable arrives. I can begin capturing. But no, the S-video end was female. So I needed a standard S-video cable to connect the Hauppauge and the VCR. No store in the whole of Tasmania had them. Electronic stores, Hi-fi stores, I emailed or phoned every likely suspect. eBay had them on the mainland, but that could take a week. So, off to the five charity shops in Devonport that sell used equipment, and then the Tip Shop (the recycling centre). Nah.

Finally got two S-video cables at another Tip Shop in another town.

Get home, connect the cable and… no signal to the Hauppauge. Several hours later, after testing all connections on all cables using a multimeter, squeezing the connectors, twisting the cable (checking for breaks), then using the VCR, my old Tube TV, a DVD player… still no signal. Then it came good. Some pin, all along, not making proper connection.

Then I started looking into how these cables work, and I can't get my head around it.

The Hauppauge has an 8-pin female socket, but I'd like to know what the pins do. I would have thought there should be:

2 for audio (grounded at case)
2 for S-video (Y and C signals)
1 for composite (Y + C as one signal)
3 for component (Y Pb Pr)

Adds up to 8. Fine… except when I was multimetering the standard S-video cable, the ground pins (photo in this article) are not connected, and they are not connected to the case. The numbers now don't add up:

2 for audio (grounded at case)
4 for S-video (Y, C, 2 grounds)
1 for composite (Y + C as one signal)
3 for component (Y Pb Pr)

Ten pins. So three of them must serve the save function. This is where I'm lost.

According to Wikipedia, Y is derived from all three original RGB signals, and is the luma, the brightness. I assume the "Y" is the same for S-Video and Component video, so those two can double up on one of the pins. So now we're down to 9 pins needed.

Ques: How do we get down to 8 pins? Which other signal has been doubled up?