Two small points we might consider while looking at this setup? Two small points may be missed. One is that we need to HOLD the switch while using it for the boost. Note that the switch is not one which clicks on and stays but is often a momentary switch which is only on as long as we hold it.
But then the confusing thing may be how this wire LR also get power to hold the mode solenoid, once we have the engine running! Wire LR has two sources of power, one from using pushing the button to start and then when the engine is running there is a connection, often called "ignition hot" that keeps sending power to LR. That power keeps the contacts of the solenoid closed to let the engine alternator charge both the chassis and the coach batteries as we drive!
But this is kind of a great thing but with potential problems? Great to let the coach get charged without us doing anything or even being aware of it. Not so great as it tends to make the solenoid arc every time we star the engien and they tend to wear ot a bit sooner than we like! Something to keep in mind if the coach battery stops getting charged as we drive!
One good reason they changed the mode solenoid with mechanical contacts to the newer BIM (battery isolation manager) which has solid state parts that don't have the arcing problem!