Sounds like maybe things are working close to right at the time you were testing. Part of the tricky side of batteries is the way they are kind of slow, when we are charging or discharging.
What we can often get into and it can confuse us if we don't keep it in mind is that we read the voltage right at some point like the post and that says what we are putting in right now or what WAS put in not too long ago. But the battery is a group of cells and it is a slow chemical reaction when we charge or discharge them.
Sometimes called "surface charge" as we are reading what is happening at the surface or posts and that doesn't tell us what may be true way down in the battery chemicals.
You are correct to let the battery set for a while to get stable after a few hours if we want the best reading for the whole battery!
So I think what you may be seeing is this? So checking may be needed as my answers are not much more than trying to see what you are doing and I can be missing the idea completely!
When you check the voltages after letting things set for a while, you are likely to get the voltage from coach being a little higher or lower than the chassis. Just the way they usually work as they are different? One thing to keep in mind is that a fully charged and fully good lead acid battery like any the normal older style car batteries will never hold a charge higher than 12.7-12.8 just because of the way the chemicals work!
Any time you read the voltage higher than that on this type battery, it tells us, you have been charging them and they are not settled down yet!
When you read 12.9 on the chassis side, that says they were not fully settled yet. No big problem, just a detail to help understand why we get funny readings, sometimes.
Then when you saw 14+ on the chassis side with the engine running, you are good from the alternator to the chassis side!
But if you shut down the engine and pushed the switch, it uses power from that battery to operate the solenoid.
So if you see the chassis side going down a little when you are pushing the switch, it likely is just that you are using some of the voltage to operate the solenoid! Part of the reason for it to look like it is going down is that you are reading right at the point where power is taken out and it dips, even when there is still plenty of power down in the battery. Let it set for a few hours and likely the stable battery will have popped back up to where you started!
Kind of like looking in a big barrel of something slow like syrup? You take a cup of syrup out and look in a little hole and you may see the level has gone down but if you wait a bit and look, the level gets stable and it doesn't look like you took any out!
When we charge we put a little "pile" of power right at that point or if we use a battery, we make a little hole? But if we wait and look later both the hill or the hole may have leveled out and we can't see we have used any or added any!
Goofy sounding but we can't see electrons, so we have to talk about something we can imagine better. I did classes for clerks, typists, secretaries that were coming into craft jobs for a while and I had to tell them about chocolate syrup for them to get it!
Sorry about the goofy stuff!
The name of the switch on the dash has gone through several different names for the same switch. Boost, AUX, or battery mode, are all the same switch!
Most are momentary and only connect while we are pushing them. A better name might be automatic jump start? If the chassis battery is weak (say we left the radio on?) we can get a jump start from the coach battery and without getting out jumper cables!
The thing that needs checked is that the battery on the left side gets connected to the right side, both when pushing the switch and when the engine is running without pushing the switch!
Push the switch for a convenient jump start!
OR expect the solenoid to connect them together automatically when the engine is running! The second part is where it should pump some power back into the coach as we move from one campsite to the next.
But keep in mind that it is a slow process and if we only drive a couple hours, it may not be near enough to go through a second cold night running the furnace.
Not knowing what made you think it was not working but if you camp and run the coach batteries pretty low using the furnace and then drive a hundred miles, that may not be long enough to get them fully back up to normal.
So if you do that several nights in a row, things can get lower and lower each night if you are not driving a pretty long way each day!
And that can be where we get tricked if we look at the voltage and forget about the hill and hole ideas!
We often get the problem of folks who have missed that part. They have the batteries run down, put a charger on for 15 minutes and see the voltage says 13.5 and think they have good fully charged batteries. They're happy to know their batteries are so good and charge up so quick! WRONG!
They go play and come back to find the batteries are only 9.5 and that's nearly dead!
So the one I might want to verify for sure is that when you check the coach battery voltage, it should come out somewhere 12+/- but when you start the engine and rev it up above idle it should run the coach voltage up near 14! When running faster or slower, you can see the rise and fall with the engine speed.
But keep in mind that is looking only at where you are putting the power in and NOT really the true battery. You may put it in at 14 but after a few hours, it will never be higher than 12.8 if it has settled fully!
One hazard of boondock camping is that it is harder to figure what the batteries are actually doing.
So simple that they can fool us every day!