Lets talk a bit about TCs:
It is a common misconception that the top of the oven is a lot hotter than the bottom. This based on the old wives tale "Hot Air Rises." Actually, it isn't hot air that rises, but the colder and denser air that is heavier and displaces the warmer air ... which floats over the cold air. This causes convection. This is largely what causes thunderstorms and affects the comfort of large rooms at 70°F/20°C. Inside a fully soaked HT oven with a cubic foot or two of closed space at 1500°F/800°C, there is so little convection gradient that it is insignificant.
Thermocouples only read temperature at the bi-metal junction that makes the tip. This fused junction creates a tiny electric current that rises as the temperature rises. The readout displays this voltage as a temperature value. Readouts are rarely inaccurate, but the TC can vary. The rest of the leads are there to get in the oven as needed. The two leads should be insulated from each other, as touching will make the reading inaccurate. Ceramic sleeve insulators is the most common method. Covering the leads with these insulators will not affect the reading values as long as the last inch of the TC is exposed. The insulators will also add some rigidity to the leads, which get pretty pliable at HT oven temps.
Be aware that the TC, the TC mounting block, the wires from the TC to the PID, and plugs/sockets at the PID are all polarized and of specific metals. Using any other wires/connectors, or connecting any with the polarity wrong will give inaccurate readings. Ovens and forges need a type K TC, and all the connectors, wires, and plugs need to be type K.
The best place to get an average reading of the HT oven would be in the volume center of the oven. This would be half way between the top and bottom and half way between the front and back. This is usually done by placing the TC tip about two inches in the chamber at the center top. Once the oven reaches the set point and stabilizes, this will be quite accurate. In some ovens, the TC is placed coming in from the rear, and projects forward along the top 6-8"/15-20cm. As long as it is in the open area of the top and not close to any coils, this will be accurate, too.
Thermocouples will slowly oxidize and "burn out" over time. This makes them slowly become less accurate. Having a spare and changing it every couple years (based on regular use)is a good idea. If you suspect any problem with the HT oven, the first place to look is the TC. Remove it and clean all connections and re-install, or just change it.
Testing the accuracy of the PID and TC is a very good idea. There are many simple tests that will show you an exact temperature. Things like the melting point of rock salt or certain metals will give a pretty good test for temperatures in the HT range. There are test crayons called Tempil-Stix that are accurate for checking within 5-10°. That is normally close enough for HT use. Ceramic shops/suppliers sell little cones that melt at specific temperatures.
Putting a second TC in the oven and having it as a read-only unit is a very good way to keep an eye on things. The TC should be the same as the one connected to the controller, and the readout can be a PID that is not connected to anything but power. One TC should always be newer than the other. If they are showing a significant variance, it means you should check what is going on.
Final note - The TC should be as robust as possible. 8 gauge leads is going to be the best. 10 gauge will work fine in most electric ovens. A proper TC mounting block is a must. I would suggest changing the block when you change the TC. Two hole ceramic spacer beads are good to keep the leads apart, but only really needed where the TC will have a long exposure and a short between the leads may happen. Excess lead length outside the oven can be cut off with no effect on the TC reading.
