All three wires need connecting to the croc clip.
I don't think the link wire on the clip is too important. Clips on some of these type of lead have it, some don't. Mine certainly don't.
I’m not sure why an XLR plug is used (all the conductors are tied at the croc-clip) although it is possible that this is for redundancy or to ensure better connectivity at the PAT end. You will have to ask the manufacturers.
There are 2 methods that PAT testers use to disregard the resistance of the test lead from earth bond measurements.
Some testers have a single-core test lead, that connects to the tester via a banana plug (as mentioned above).
On these testers, the user must perform an operation to null the lead. The tester will then automatically ignore the resistance of the test lead in any earth bond measurement. If a different lead, of different length etc., is used, the user must perform this 'lead null' operation again.
Other testers use what is known as the Kelvin or 4-wire method.
A much better explanation than I can give can be found here: http://www.allaboutcircuits.com/vol_1/chpt_8/9.html
Sooooo.... if you take the Kelvin circuit from that link, and imagine how it's used in a PAT tester:
Internally, both the current-carrying wire and the voltage wire from one side of the circuit are connected to the earth pin of the 13A socket on the tester.
On the other side of the circuit, the current-carrying wire is connected to 2 of the pins on the XLR socket, the voltage wire connected to the remaining pin.
The test lead takes these, and then brings them all together at the croc clip.
So there are your 2 measuring points, the earth pin of the appliance's 13A plug, and wherever you attach the croc clip.
Doesn't matter how long the test lead is, as long as all the wires from the XLR are connected to the croc clip, the tester ignores the test lead, and only gives you a resistance reading between the plug earth pin and the croc clip attachment point.
I imagine that 2 conductors are used for the current-carrying part, so as to reduce any potential overheating in the test lead.
Hope that's made the method a little clearer!
PS. don't get too hung up on the description of the special Kelvin clips in the web-link. These are used for extreme accuracy, so you wouldn't really expect to see them on a PAT test lead!