Here is a blurry picture of the clips on the backside of the four pin connector. The clips on the twelve pin connector are exactly the same. Be careful not to bend it too much as it might break:

Here's a picture of the twelve pin connector with the wires extracted (and the connecter reattached):

I happened to have an old CD-ROM audio cable laying around and I noticed its small four pin connector was identical to what is used here, so I installed the four wires I extracted into that connector. This step isn't necessary but I thought it would keep things looking clean and relatively professional:

Next I found some solid network cabling and extracted the wires from it. I also extracted the pins from an old VGA cable I had laying around:

Then I soldered the pins to the wires:

Then I inserted the pins into the two four wire connectors and used some shrink wrap to make a harness in order to keep things neat, tight, and free of electrical shorts. I also took the time to install a zip tie to keep the wires that remained on the twelve pin connector from flexing. A hardware issue with these is that as you move the throttle the wires flex at the connector causing buttons to quit working intermittently and causing the trims to do crazy things. You want to keep enough slack on the wiring going up the throttles so that it isn't stretched at full throttle, but you want the wiring at the connector to not move at all while moving the throttle. This is where the zip tie comes in handy:

Here's another look at my harness except this time connected to my network connector. The female pins for the serial adapter worked out great as I was able to slide the stripped ends of the wires into them and crimp them tight. Then I heated it up with a solder iron and the solder flowed right into the slots on the sides of the pins keeping everything nice and secure:

I suppose that if I had planned it better I could have made something work that didn't require so much soldering but it's not a big deal. The biggest problem I have now is that if I take it back apart I have no easy place to simply unplug it but the network plug fits tight enough to not move while plugging in the cable, but loose enough so that I can push it out if I ever have to disassemble it again.
When reinstalling the base don't forget to reconnect the larger vertical four pin connector:

And here's a final shot of the rear of the throttle:

Once you get to this point you can connect the throttle back to the stick with the original serial cable (don't worry about the new connections just yet) and make sure all of the buttons still work. All of the axes will still be present, but will be 'stuck' at 50%.
The rudders themselves are much easier to modify. Since there are no circuit boards or processing chips involved you can simply tap into their 9 pin serial connector. Also the fact that there are no buttons on the Rudders makes things even more simple. No dis-assembly required! There are only five pins you need to access.
OK so you're thinking that this is all fine and dandy and all that, but “how do I know what wire goes to where?” I've created an easy to use chart for you. What type of wire you use and how you do it isn't so important as is making sure the right wire gets to the right connection. The wire colors of the chart are the same factory wire colors used in my G940.
The throttle trims (R1 and R2) use black, white, pink, and light blue wires. The throttles themselves use black, yellow, dark blue, and red wires. Make sure you don't confuse the black wire used for the trims (1) with the black wire used for the throttles (2). In case you haven't figured it out, “W” stands for “white”.
For the rudders, instead of colors I used pin-out numbers. I didn't feel like taking them apart just to get the wire colors:

Here's a picture of the BU0836 controller board. It's VERY tiny and comes with connectors. I found that soldering to the connectors proved to be a pain in the rear and I ended up using a USB motherboard connector and a speaker wire connector to make the rudder connections:

This is the BU0836 fully connected. Yes, it looks rough because I haven't purchased a project box for it just yet but I will soon. Mainly I wanted to get everything connected and make sure it works. You'll notice that my wire colors don't match that of the diagram but that is because the wiring that came with the adapters don't quite match up. What's important is that the proper wire gets to the proper terminal of the BU0836 board:

Here is a run-down of how it shows up in the device manager. This is Windows 7 but I see no reason why it wouldn't run on Vista or XP either. No drivers had to be installed. It's a simple matter of calibrating and you're good to go:

Last but not least here's a final diagram of how everything is now connected to each other after the modifications are complete:

The reversal bug is NOW GONE!
I hope you've enjoyed my write up! Feel free to contact me at thereisnospoon@ympsa.com if you have any questions!