I'm not giving up on this. (Tom, you're cracking me up with the smoke bit. I wasted a good half hour reading all that.
Well, I had to step away from the car for two weeks to take my family on vacation (priorities, I suppose, ha). Glenntwincam, you are right, there is an additional sensor on the bottom of that housing. I pulled that sensor, measured the resistance across it cold (about 2,000 ohms), then boiled it, and it dropped to about 600 Ohms which is consistent with correct operation (see here:https://csr175.wordpress.com/2013/12/21/recalibrating-the-water-temperature-gauge/ ).
Also, I pulled the gauge again, and set up a 12 volt source (8 batteries in series at 1.5 V each), and then applied voltage to the sensor wire input to the gauge. And lo and behold, it works just fine. At 1.5 volts to the sensor wire, it goes full scale, at 3 volts, about halfway, at 4.5 volts, no real movement (again consistent with the above link).
So at this point, I have confirmed the right coolant temp sensor, confirmed that the temp sensor works, and confirmed the gauge works. So it's now somewhere between the sensor and the gauge, for which I could still all use your collective intelligence. (I searched for a Zetec wiring diagram for Caterhams, no luck.)
The temp sensor on the engine has two wires coming from it. One is just a grounding wire (because the housing its mounted on is plastic, so doesn't provide chassis ground.) The signal wire disappears into the wiring loom. The wire that emerges under the dash that plugs into the gauge is a different color. I'm assuming in between these two wires is a unit that converts the voltage to something that the gauge can respond to. I don't know if that's a separate unit or the ECU. Can anyone help here?
The burning smell that I smelled on the drive when all this stopped working is starting to concern me. Anything you can enlighten me on would be much appreciated. I'm gonna go start pulling fuses and checking to see if any of those are burnt out.
Thanks to all, you've all been extremely helpful.