.The switch is "made" when it fails. The physical switch on the rotary seems to operate as expected, making and releasing as the mechanical flag passes.
I am not sure I understand "made", "active", or "released". Can you describe the behavior in terms of "open" and "closed"?
I am fairly certain (but not 100% certain) that the home switch will be activated (mechanically tripped) only briefly near the home position, and that it will be wired using normally-closed contacts.
That being the case, the input should be closed most of the time, and open in a narrow range near the home position.
On the Alt-i screen, a closed input will be Green, and an open input will be Red.
If the input is remaining closed (Green) when it should be open (Red), then perhaps you have fluid contamination in the switch. Perhaps the fluid in the switch is just conductive enough to sometimes make the switch seem closed when it is open, and sometimes not.
With the rotary axis interface plug unplugged from the RTK3, you could try measuring resistance between pin 1 (the rotary home input) and pin 2 (the input common). See page 14 of the attached manual. You could also test whether shorting and un-shorting pins 1 and 2 on the RTK3 header reliably causes INP30 to change from Red to Green and back.