Temperature sensors are by far the least reliable sensors on the engine, and the TIT/EGT are the least reliable of temperature sensors due to the high temperatures and vibration they must endure.
This is dredging back many years, but I'll give the old memory neurons a try.
Modern instruments seem to use K type (chromel/alumel) thermocouples everywhere when in years past they were only used for high temperatures. They have poor output signals at lower temperatures (as with CHTs and Oil temp). Oil temperature used to be measured with Copper-Constantan thermocouples because of better output characteristics at lower tempera. tures.
Now with sensitive digital electronics capable of handling non linear calibration curves and tiny input voltages, even these little little signals are enough to be detected, corrected for non-linearities, and then used for sufficiently accurate displays in our planes. So type K is being used more and more.
However......
Measuring comparatively low temperatures (compared to EGT/TIT), these tiny signals can be easily fouled up by dirty connectors, intermittent connections caused by the small but stiff thermocouple wire wiggling and breaking, and other mechanical and electrical resistance faults. It is just the nature of the beast.
My MVP 50 engine monitor reads OAT from a thermocouple in my cabin vent NACA duct, and last flight decided to start indicating numbers way above and below the real OAT. Looks like a classic intermittent connection problem. I checked the probe wires today (easy to get to) and wiggled the connector on the data box (hard to get to) while a friend watched the readout, but we could not induce an error. Also classic intermittent behavior. My bet: it will show up next flight, or the flight after that, after a bit of vibration exposure. Or it could be a short in the thermocouple wiring somewhere which creates a secondary thermocouple at the short (different location and temperature) that fouls the output of the primary thermocouple. As noted thermocouple wire is stiff and difficult material, not forgiving like multi-strand copper.
Bottom line: suspect connections and wiring as much as the thermocouple junction inside the sheath or fitting. Check for large enough service loops to absorb vibration, but not so long as to allow the wire to flex between tie downs.
Fred Moreno