Sorry if my posts are rather long-winded. I believe if you understand how the system is supposed to work you will have more luck troubleshooting it.
The fuel sending units after 1964 until the end of production operated over the same resistance range. This is nominally 30 or so Ohms for full to about 270 Ohms for empty. That was true regardless of Smiths or Nippon Seiki gauges.
The temperature sending unit is the one that screws into the head and it is located near the thermostat housing. You have identified it correctly regardless of the wire color. (As a future note... black is a particularly bad choice for a replacement in Lucas wiring schemes. Black is used for earth wires which this clearly is not). Yes, to short it to earth you only need to connect it (directly or indirectly with a wire) to a bare metal spot on the engine block.
I have not had the opportunity to work with Nippon Seiki gauges but I expect their needles to go "above" the top mark when their sending unit wires are shorted to earth as that is what the Smiths gauges do. Consider for a moment the case of the fuel gauge. As I mentioned, the nominal fuel sender resistance for full is 30 Ohms. When you earth the green/black sender wire, the resistance to earth goes to "0" (or pretty darn close). Therefore, more current flows through the circuit and that makes the needle go "above" the highest mark on the gauge scale.
You said that with the external voltage stabilizer connected to the flex circuit your gauges now read wrong even when the sending units are disconnected. That says something is wrong but without seeing your gauge cluster up close I doubt I could tell you what is wrong.
You cannot measure the output of a electromechanical voltage stabilizer (Smiths or Nippon Seiki) directly with a multimeter. The unit switches on-and-off several times per second so there is a voltage continually swinging between 0V and 12V. WIth the points in your Nippon Seiki voltage stabilizer held apart by tape and the external voltage regulator connected to the cluster you WILL be able to measure the voltage at various places to confirm you have wired the regulator correctly. Specifically, turn the key to the run position AND disconnect BOTH sending unit wires and keep them from touching earth. Use a multimeter to measure between the terminal on each disconnected wire's end and earth. Each should measure 10V if you have wired the external voltage regulator correctly.
The following is a short explanation of what is supposed to happen with these gauges (both fuel and temperature).
You turn the key to the run position. 12V is supplied to the voltage stabilizer. The stabilizer's job is to reduce that 12V in to a nominal, average 10V output. The 10V output goes into one side of the gauge (either/both gauges). Inside the gauge is a resistance wire wound around a bimetallic strip connected to the gauge needle. The other end of the resistance wire is connected to the sending unit wire. The far end of the sending unit wire is connected to the sending unit itself. The sending unit is a variable resistor. The other side of the sending unit provides an earth connection either directly by its mounting threads (temperature sender) or via a wire to earth (fuel sending unit). Current flowing through the circuit causes the resistance wire wrapped around the bimetallic strip connected to the needle to heat up. As that bimetallic element is heated it bends and moves the needle. The sending unit "throttles" the flow of current and thus changes the amount of heat the bimetallic strip sees.
So... if your gauges are moving up off zero with the external voltage regulator connected AND the sending unit wires are disconnected at the same time... something is seriously wrong with the circuit. Again, I doubt I could tell you what is wrong without being there in person.