To complicate things further airframe manufacturers may label the gauge with a generic name that does not reflect the actual thermocouples' location. For example on the 747 it is always labelled EGT when in many engine models it is not truly EGT.
On the JT9 series all engines except the -7Q and -7R were ITT however Pratt and Whitney relocated the probes on the -7Q and -7R to the LP turbine exit making them EGT rather than ITT. The result was max EGT on the earlier models was in the 900-1000 degree range but on the -7Q & -7R max EGT dropped to the 600-700 range in spite of being more powerful. engines.
With regard to TIT probes on the T56, having boroscoped many 501D13's (the civil equivalent on the Lockheed Electra) in my youth I can assure you finding melted/bent rearward thermocouples was not uncommon. Max TIT was in the high 900's and being a standard day engine it was always at max TIT if the OAT was above 15 celsius.