I know from first hand recent knowledge that a type K does not work with the type E old style gauge we have in our aircraft. The reason is the value of the signal is stronger in a type E than a type K. A type E system must be entirely type E. The problem is the probe, the wiring and the gauge must be the same. That also applies to the K. No mixing of systems. Try this link for further details. Perhaps I misinterpreted the information.
https://alcorinc.com/index.php/troubleshooting/