Why TesysT logic inputs are unexpectedly activated if nobody activated pushbutton connected to logic input?

It can happen due to very long cables connected to a logic input. This problem is more frequent in the case of AC signal than DC signal. Long cables (over 50m) have a capacitance that is significant enough for flowing the leakage current that can unintentionally activate TEsysT logic input.
Solution:
Use shorter cables
Use LTMR...BD instead of LTMR..FM. DC signal has a lower leakage current than AC.
Use interposing relay. The coil of the interposing relay has a lower impedance than the TEsysT logic input and so a greater current in the connected signal cable is needed to energize the relay. A push button installed far away will activate the relay (the relay must be close to TEsysT) and contact from the relay will activate LTMR logic input.
Add a resistor to each LTMR logic input.

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