I have this crimp tool, can't remember where I bought it from:
https://www.techtoolsupply.com/Sargent-Open-Barrel-Crimp-30-16AWG-p/ros-1026ct.htm
It did an OK job, think I only had to redo one or two crimps that didn't clamp well enough. It took a bit of trial and error and a few wasted crimps to figure out a good process - IIRC I used the next size up to get it started, then switched to the smaller size to finish off.
A hacky alternative would be to fold the tabs over and solder, followed by folding the tabs for the insulation part. Or to fold over then use a centre punch to get more squish. Can't say I recommend either approach!
A bit late from me, but thank you for your help. I made the wire one night, it didn't work, and displayed the same problem as before. Obviously I didn't think it reasonable to believe I made the wire in the same way the other one was broken; I assumed the motherboard was broken somewhere and was not a happy camper.
Nevertheless, I knew my crimps weren't really all that good to begin with, so I picked it back up a few days later and re-crimped a lot of the wires that kept coming undone. Finally, I felt happy with the wire(although it wasn't the prettiest), and amazingly, it finally worked!
For everyone else, a bit more about the specific problem I was having:
Ever since I bought the wheel(refurbished off ebay mind you), the paddle shifters would only register as an input if the wheel was turned within probably 180 degrees of center. Anything more than that, and they simply didn't work. Since I was clueless about the wheel's construction at the time, and didn't bother to think about it any deeper, I just assumed that was down to the way logitech made it, and because it's an entry level wheel.
But after a long session of hard drifting, the problem got worse, with the buttons all pressing randomly whenever I turned the wheel, and finally the buttons being completely stuck on with no input. This is when I knew something was wrong.
I took the wheel apart, narrowed the problem down to the "problem wire", and found this thread.
Took me a couple months of procrastinating, but I finally got around to fixing it.
To anyone else who has this problem:
Follow Outspacer's instructions and links. The ribbon cable worked, and so far I haven't had any more issues.
Tip for newbies at electrical work(like me): BUY EXTRA. It's all super cheap, and it's totally worth it. I bought six feet of cable(you only need around 2-3 for one length), 10 connectors, and the 100-pack of the crimp pins. I am very glad they force you to buy the 100 pack, since as a newbie I went through A LOT. Another benefit of buying extra is, if you ever have to re-make a wire that breaks again, you have the materials and tools and NOW you have the know-how to do it better.
This is the crimp I bought:
https://www.amazon.com/dp/B078WNZ9FW/?tag=gtplanet-20
I think I used the second smallest and the third smallest holes on the crimp for this job. When crimping the wire itself(the actual conductor), you want to crimp quite hard, about as hard as you can. But when you are crimping the insulation, you only want to firmly clamp it, not enough to dig the crimp right through it. If you crimp the insulation too hard, it splits the entire wire and means you have a bad connection and the wire is prone to easily being pulled out of the crimp pin.
There is a bit of a technique to using the crimpers, and the items you're dealing with look a LOT bigger in the pictures. Be easy on the crimp flanges until they wrap back on themselves while crimping or you might pop the flange right off. When attempting to crimp the insulation after the main wire crimp, the act of crimping the first crimp usually pinches the wire away from the end of the crimp pin; I found it helpful to hold the wire with my thumb and middle finger and steady the end of the pin with my index finger, putting some pressure on the wire to fold it back towards the pin a bit while crimping.
One more thing, you NEED the crimp for this. Buy the crimp along with all the electronic items and save yourself the frustration of trying to crimp with needle-nose pliers like I did. It doesn't work at all.
I thank all the posters again for their insight in this issue!
I'd messed up the chicane, but I don't think I was any more violent with the wheel than normal.
Rash would be buying the T300 with Alcantara rim that's now about £310, that I didn't buy before because of Thrustmaster's reputation for unreliability - ha!
Wouldn't recommend it to anyone who doesn't have relevant competance and a suitable crimp tool though 
