Does a thermocouple conductor have a direct current resistance requirement?
Often, in modern usage, there is only a fairly generous maximum resistance, at least in the hundreds of ohms, and even that is mostly because it's desirable to pass a small current through the sensor in order to determine if it has failed. In heating applications the current is usually in the direction which causes a positive offset in the temperature reading, which is usually (not always) the safer direction. Without that protection, any amplifier will have a bit of bias current which also needs to have a path. Since the voltages being measured are of the order of microvolts or millivolts, even a small current can result in a measurement error with a relatively small resistance. The protection current should also be reasonably high because thermocouples are often used in non-ideal situations with contamination, soot, liquids etc. present, so perhaps in the low hundreds of nA.
Some simple electromechanical pyrometers have a meter movement coupled directly to the thermocouple, in which case there will be a specified resistance for accuracy (for example, 10\$\Omega\$, typically marked on the meter scale). Such devices have become more rare as the cost of electronic solutions drops but they can still be found.
Thermocouples and thermopiles used to directly operate fuel gas valves (a safety consideration so the flow of gas will be stopped if the flame goes out, thus avoiding the gas accumulating in a mix with air and eventually finding a source of <<bang>> ignition) need very low electrical resistance.