I've already done an instructable describing how to open and clean a ColecoVision, so read that for instructions. Opening a ColecoVision is a bit tricky, so definitely check it out.
And you should probably clean this sucker. Seriously. If it hasn't been opened for 30 years, there are probably some horrible, nightmarish things in there that you don't want in your home. Send your loved ones on a day trip, make sure you're up-to-date on your immunizations, put on your HAZMAT suit and purge this thing of its horrors.
We're going to make a very simple circuit. I'm not entirely convinced that this is the best circuit to use (though it works fantastically), which is part of the reason I opted to use a separate PCB and run wires. If I decide later to try something else, it will be easy to remove this.
What we're going to do is two things: amplify a composite signal with a transistor and tap into audio out.
There's nothing to stop you from breadboarding this first. I decided not to, since it only involves three components, but feel free to if you're more leery.
See the schematic. A brief run-through: Wipe of potentiometer gets +12V. One leg goes to transistor's collector. Base of transmitter goes to Pin 13. Emitter goes to video out; also to 1k resistor which goes to ground.
Meanwhile, just run audio out from the marked solder point.
When you're done soldering the PCB and all wires are connected, put some electrical tape or hot glue on the bottom to prevent any shorts.
Next, solder the outputs to your jack. How do you know what terminals to solder to? The easiest way to tell is to use a multimeter to test continuity. Plug the TRRS cable into the TRRS jack and check to see what terminal connects to which connector. Be sure to find Ground as well.
Check and double-check those connections. Draw a diagram if you have to.
Then solder them up. Composite and Ground come off the PCB. The audio comes straight from the board. I ran two wires to do 2 channels of audio. You can probably run one wire and solder it to the Left and Right terminals of the jack for the same result.
Considering what a pain the ColecoVision is to open and close, now is a fine time to test the A/V out. Plug it into a TV, plug in the power, put a cart in and turn it on.
If you're getting a poor picture or no picture at all, try adjusting the potentiometer until it looks good. If it still doesn't work, go back and double-check that everything is correctly soldered. Check for any possible short-circuits.
When you're satisfied with the video and audio, mount the A/V jack then close the sucker up. You may want to use electrical tape to route any wires that may stray near the cartridge slot.
Drill a 1/4" hole in spot that will allow the plug to fit. Then mount the jack in whatever way it is supposed to. Mine used a nut to hold it in place.
Close the console up, replace the screws and you're good to go! If you really want to bask in the greatness of this upgrade, go ahead and switch between composite and RF. Force your friends and family to watch. Demand they be awed. Then apologize profusely, because that was a pretty rude thing to do.
Some final notes:
If I were to do this again, I might opt to not use a PCB and just solder the components directly to the RF board. It's such a simple modification that a PCB is a little overkill. I'd also use much shorter wires, and possibly better-shielded ones, though they haven't given me trouble yet.