Sorry for the late response. I've dug into both the III and earlier version remote triggers. It's very simple to adapt the cable to a shutter release of your choosing. The Black and the White wires are all that's required to trigger the camera. The Red wire I believe is a wake signal to turn on the light meter in the AE finder so I've disregarded that. I'm also not entirely sure if I'm correct about the Red wire since I don't have the AE finder to test with.
I wanted to be able to quickly change over from a wireless remote to a wired remote so I used 1/8" male and female connectors mid-cable. When I need long exposures I use a dirt cheap wired remote with a locking feature. When I want a wireless trigger I use a Vello Shutterboss wireless trigger. The wireless trigger does not allow for Bulb exposures, it's simply a quick single pulse operation without reworking the microprocessor.
I had thought that a resistor would be required, and it may actually help, depending on the internal resistance of the trigger you choose, but things are working well without one in my set up.
When the remote is depressed the voltage drops across the Black and White wires from +5V to Zero. Black is ground, White is +5V.
Knowing that only the Black and White wires are required means it's simple to make a non III remote work on the III body, which I've also done.
As a double check on your cord before you wire things up, if you check continuity with a meter you should see that Black and White should correspond to pins 1 and 2, respectively on the plug, counting clockwise with number 1 as the first position to the left of the largest of the three keys on the plug, at the bottom center. If you want to play around with the camera body itself, don't forget to reverse that order, Black being pin 8 and White being pin 7 on the body.
The only trouble I had with my customizations was finding a connector that could accept the thick cord of the 680 remote. I also wanted something that looked less cheesy than the usual suspects for 1/8 connectors. Googling 1/8" jack images turned up the ones I'm using. They look good but could be built better as they lock together a bit wobbly, but still work fine.
(edit: the connectors I was using were giving me trouble with maintaining contact so I swapped them out for some cheapos and things are working fine now).
I've also made a custom AA battery holder from a cheap battery holder box and the cover on the 680 battery compartment. Let me know if you would like those details.