Okay, lemme see...
Starting on the 120v AC input side.
Looks like a black coming in and going to the gray wire nut, which then feeds into a 120v push-button breaker (above the 120v receptacle on the face plate).
The neutral (white) that goes with that incoming hot goes to a yellow wire nut. The bare goes to the ground bus bar.
Then, on the other side of the breaker, is one black feeding down to the receptacle, and another black that goes through the grommet in the dividing wall.
The incoming neutral goes to a yellow wire nut, then from there to the clear crimped on "hat" connector just next to the breaker. From the hat connector there is one neutral down to the receptacle, and another goes through the grommet in the dividing wall.
So, the original incoming connections TO the unit from shore power, are the black wire that is in the gray wire nut, and the white wire from the crimped on hat connector.
At some point (probably when the camper was built), someone tapped in to feed another 120v "something" (probably another receptacle). They piggy-backed that yellow wire onto the output side of the breaker. where it runs over to the yellow wire nut and connects to an outgoing black wire. When they did that, is also when they put all the neutrals under that one yellow wire nut. (Originally, there were probably two grey wire nuts - one to connect the incoming hot to the breaker, and one to connect the incoming neutral to the wire from the crimped hat connector.)
So, the 120v receptacle in the face plate of the unit and the black wire that feeds through the grommet - and the piggy-backed yellow - are all protected by that push-button 120v breaker.
Thus, if that breaker is tripped or non-functional, there will be no power to the face plate receptacle, or the 12v converter section - nor the other whatever it is that is fed by that yellow wire.
I see no problem with the 120v side of things - it all looks to be wired properly.
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Now, going to the other side of the dividing wall to the converter section, we see a black and white coming through the grommet. I can't see where the white goes, but the black obviously goes into a crimped on hat connector. I'll assume the white does as well.
Those are the 120v that feeds IN to the transformer in the converter section.
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Coming out of the transformer, we've got a blue that goes through a metal wall and feeds one side of the switch.
The other side of the switch is fed by a red wire which comes from the fuse block (and battery).
From the center of the switch, we've got an output that goes through the fuse holder and feeds the lights and furnace.
When the switch is one way, the lights and furnace (loads - center of switch) are connected to the fuse block / battery. When the switch is the other way, they are connected to the transformer. When the switch is centered, the lights and furnace are connected to nothing.
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Okay, so here's the problem...
Flip the switch one way and the output from the transformer (switch set to "converter") is connected to the lights and furnace. Flip the switch the other way, and the fuse block / battery is connected to the lights and furnace.
But at no time, is the output from the transformer connected to the fuse block / battery.
So that unit can draw 12v FROM the fuse block bus bar, through a fuse and can then connect that incoming 12v from the fuse block to the lights/furnace with the switch.
It can also draw 12v from the transformer and connect that to the lights/furnace with the switch.
BUT, the output from the transformer (converter) NEVER gets connected TO THE FUSE BLOCK / BATTERY! It only pulls from the fuse block, it does not push toward it. It sucks, but it doesn't blow! D'oh!
So the transformer will never power the loads connected to the fuse block - NOR will it charge the battery of course, since the battery is connected to the fuse block.
That unit was never designed to charge a battery at all.
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But maybe we can fix it.
What we want to accomplish, is to have the output from the transformer connected both to the lights and furnace as they are now, and ALSO connected to the fuse block / battery.
The simplest way to achieve that, would be to use a doohickey. Doohickeys rock - they are far superior to widgets and gizmos. We could use one that looks like this:
We could stick the doohickey on the center terminal of the switch, put the blue wire to the loads on the doohickey, then pull the red wire off the end of the switch and double it up on the doohickey with the outbound loads wire.
So we'd have the wire from the transformer feeding into the switch, and the output would go out the center as it does now - where it would feed the blue wire to the furnace/lights, and ALSO feed the red wire to the fuse block.
Thus ALL the loads - the fuse block as well as the lights/furnace will be fed continuously from the battery (though the lights/furnace would still go through the fuse on the front panel).
AND when the converter is powered up by shore power, it will supply up to 9a to the "12v system". If your running loads are less than 9a, then it will trickle some power to the battery until the battery reaches 12.5v.
If the switch were in the off or battery position, then the only result would be that the TRANSFORMER is no longer connected to the "12v system". The feed from the fuse block / battery to the lights/furnace would always be active.
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HOWEVER! That doohickey setup might be a VERY BAD IDEA!!
There might be an actual reason - other than blatant nincompoopery - why they built the unit the way they did. The only reason I can think of is that the transformer is not protected from backfeed from the battery.
It might be a very bad idea to connect that transformer to the battery...the battery might do something horrible to the transformer. If so, then they way they did it - with a switch so that the transformer and battery can never connect to each other - would be the correct solution.
And that's almost certainly why that switch is there...
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So now what?
Well...the "proper" way to wire that thing up, would be to connect the fuse block to the same place as the lights/furnace (output from center of switch through fuse to lights/furnace/fuse block) and then instead of running the battery to the fuse block, run it to the red wire off the switch.
Then, ALL the loads would be powered EITHER by the transformer, OR the battery, but "never the twain shall meet".
That would be proper - but the converter is JUST a "converter" it is not a "converter/charger". In that configuration...it will not charge the battery.
Which is was never designed to do in the first place.
But you can pick up a battery charger and feed it from the incoming shore power, so when connected to shore power you'll be running the loads (up to 9a) from the converter, and charging the battery.
But...
If you do that, then you don't need the antique converter anyway. Just connect the battery to the fuse block as you have it now, move the lights/furnace loads over to the fuse block, and then connect the battery charger to the battery.
Then, all the loads run from the battery all the time, but when you've got shore power to the battery charger, it will supply up to X amps (whatever size the charger is) to the "12v system".
That is what I'd do.*
I would also add a switch (simple SPST on-off switch) between the battery breaker and the fuse block. That way, I could just kill all the loads by flipping the switch, but still have the battery able to charge when there is shore power.
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(*Well...not really. What I'd actually do is try the doohickey hack first. IF that results in letting all the magic blue smoke out of the transformer - THEN I'd rip out the converter and go to the battery charger setup.
But of course, no one should never do what I would do. M'kay? <insert rapidly spoken legal mumbo-jumbo about liability and fire and hazardous to life and limb and why oh why didn't I take the RED pill>. I'm a lunatic, m'kay? Don't do what I do, m'kay?)