If the cross-connect signal is verified to not be on, then it sounds like the LI-BIM has failed or is miswired. The chassis battery should not continuously sit at 14.6
One check is to carefully lift and tape the wire labeled SIGNAL on the BIM, then see if the voltages drift apart.
If they do drift apart with "signal" removed, then you need to investigate the signal wiring. Either ground or +12V on the signal line will cause it to connect. Signal needs to be "floating" for normal operation.
If they do not drift apart, then the BIM is suspect.
There is a functional test procedure for the regular BIM posted on FRF, but not the LI-BIM. I do know that while driving, with some load on the house, the LI-BIM seems to follow a 15 minutes connected, 15 minutes disconnected cycle. If your house just tracks the alternator voltage continuously for greater than 15 min driving, then that would be a second indication that it is not functioning. Again, with signal removed and safely taped, to isolate any switch effects.
2021 Isata 5 28ss 4x2 / 2020 JLU Rubicon
Prior: 2016 Lance 1995 / Ram 1500 Eco Diesel
2012 Lance 1575 / 2015 Jeep JKU Rubicon