Robert, I've added to pic with descriptions. My Bird had the GENSET input disconnected. The GENSET input was designed to OPEN the Big Boy relay for systems with generators that couldn't charge both chassis and coach batteries at the same time. It's a 12V input same at BIRD IGNITION input. I'm assuming this GENSET input is also not used on your coach. Just splice one of the 2 IGNITION wires (doesn't matter which one) with another wire+terminal and attach to GENSET input. That is the only BIRD change.
Intellitec support confirmed the above mod seemed like simple solution to what I wanted to accomplish. He warned one issue may be that due to higher resting voltage of Lithium compared to my AGM that my lithium would charge AGM continuously when running on battery only. I tested this and did not find it to be the case. After a full charge, the resting Lithium voltage is a little higher than AGM and I found my Lithium charging my AGM at 1-2A... but after an hour or so both batteries banks were discharging. The lithiums discharge at a higher rate - but no cross charging after an hour. That 1-2A for an hour or 2 is really nothing and doesn't seem like it should be a problem. Seems any system with mixed batteries like this will have the same issue unless you completely isolate the 2.
Another item to be aware of. When you turn ON the ignition switch on there is a 1-2second delay before Bird detects the condition and opens the Big Boy relay. I discovered this when reviewing my logs and noticed that one time when I quickly started the engine to move the coach a foot there was a large draw (360A) on the Lithium .. this was due to engine starter pulling current from the Lithium. This really shouldn't be a problem as long as BMS in Lithium doesn't trip. To avoid this I just turn ON ignition and pause 2 seconds before cranking.
As I've said before the logging capability of the Thornwave monitor allows me to literally pull logs from weeks back and review voltage, currents, power draw, temp, SOC, etc. I highly recommend it or something similar to be able to make sure everything is good with your setup.