The SPOUT (SPark OUTput) connector is the little plug on the wires going into the TFI module on the distributor. You have to pull it out before setting the timing. Pulling it eliminates the timing advance function by disconnecting the ECU from the ignition system. Technically it connects pin 36 of the ECU (the electronic engine control unit or computer) to the TFI (Thick Film Integrated circuit) module on the side of the distributor. The ECU picks up the timing pulse from the PIP (Profile Ignition Pickup) or Hall effect pickup in the distributor and varies the ignition timing depending on what the engine sensors tell it. The ECU also uses this signal for adjusting fuel injector flow. The advanced or delayed timing signal is sent back to the TFI through the SPOUT connector and then to the coil where it causes the sparks and to the tach (the little green wire in the plug on the coil). Note that the TFI has a starting mode wherein it will send the PIP signal directly to the coil bypassing the ECU so that the coil will spark and the car will start before the ECU comes to life. This mode has no advance and operates at the basic timing setting of the distributor. It is this mode that lets the car run without the SPOUT connector in. Also, if the ignition timing circuit (the SPOUT driver) in the ECU is dead or grounded, the car may run with the SPOUT connector out (which bypasses the ECU) but not with it in. So an ECU failure can act a lot like the partial PIP failure I had. But ECU failures are reported to be very rare. In fact, I am told that "rebuilt" ECU's sold at autoparts stores are really just cores and used units recovered from salvage yards that are tested and resold. They charge a $90 core charge because most of the trade in cores are actually still good and they are just resold (for about $125). Usually the problem is in one of the sensors, the wiring, a ground or the PIP in the distributor as in my case.
I have not seen a explanation of what the TFI module is doing but my impression is that it is basically an amplifier taking the faint signal from the PIP/hall effect pickup and/or the ECU and amplifying it into a pulse which will trigger a spark through the coil. Which is why itneeds a heat sink. And that would suggest why the PIP signal can be too weak to make the ECU spark output driver work as it is probably a digital device which needs a certain voltage threshold, whereas the TFI can still amplify even a weak PIP signal enough to make the coil spark. So a weak PIP will run the car with the SPOUT connector out but won't run it with the SPOUT in and the ECU engaged.