I see lots of responses, but not a lot of maths. So here I am to ruin everyone's morning! Scroll to the end for the TLDR.
Let's try a few methods and see!
According to this hastily-located fuse diagram I found in a YouTube video (and YouTube never lies), the 200 has 30A available on the towing plug before it blows the fuse. Staggrlee corroborates this info. Consult your documentation, but this should be sufficient for our example. In the documentation, it shows that other trailer loads like the brakes and lights run on different wires, so I will assume that we have all 30A at our disposal for our analysis.
Fuse box diagram (location and assignment of electrical fuses) for Toyota Land Cruiser (200/J200/V8; 2008, 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017, 2018).
fuse-box.info
View attachment 3377465
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First, could you run a wire from this pin to the battery in your trailer directly? Let's try some math.
The current (I) flowing between two points can be determined by knowing the voltage difference between those two points, and the resistance separating them:
V1 = Alternator output (or start battery voltage, whichever is higher at a given point in time)
V2 = Voltage at the trailer battery
R = Resistance in all of the wires and connectors
I = V2-V1/R
Let's model the case where you're just starting up the vehicle after sitting for several days and the battery in the trailer is dead from running the fridge. That's a very feasible worst-case.
For V1, our alternator voltage, I've never measured higher than 13.8V, but we'll round up a bit for some safety factor.
V1= 14.0V
For V2, we'll look at the SnoMaster's cutoff. 10V and 10.7V sound like they're getting into deep-cycle territory, so I wouldn't run a SLA down to those voltages. We'll stick with the 11.8V setting.
View attachment 3377469
V2 = 11.8V
For R, since we're modeling for a worst-case scenario, I'm going to ignore any resistance introduced by connectors. I'm also going to assume 12AWG wire throughout. I'm using 16 feet for the run of wire within the Cruiser, 5 feet for the tongue, and 5 feet inside the trailer.
www.cirris.com
View attachment 3377470
R = 0.033ohms
Plug those all in:
I = 14.0-11.8/0.033
I = 66.6 Amps
But, we said that the fuse for the trailer would blow at 30 Amps. 66.6 >> 30, so the setup where a wire is run directly from the tow plug to the battery won't work

And we proved it with math!
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Second, let's evaluate a DC-DC running from the tow plug.
30 Amps lets us choose from a few models mentioned above.
The Victron
https://www.victronenergy.com/uploa...Smart-DC-DC-chargers-isolated-250-400W-EN.pdf
The Renogy
12V 20A DC to DC On-Board Battery Charger - https://www.renogy.com/12v-20a-dc-to-dc-on-board-battery-charger/
The Redarc
https://cdn.intelligencebank.com/au/share/yE9N/zJpl/oGLrq/original/BCDC1225D,+BCDC1240D+Manual+English
I'd like to note that the documentation for the Redarc is much better than the other two. Good on you, Redarc. It's also the highest current of the lot, so if it checks out, the others will work as well. For the example, I'll be using the BCDC1225D (BDCD for short).
To evaluate this setup, it's clear that the 25A that the BDCD draws is less than the 30A the fuse is rated for. Huzzah! But the concern noted by some sharp commenters above is that it's possible that the voltage seen at the BCDC will sag to the point where it shuts itself off when there's high current on the wire. Let's see.
We want to know voltage drop, so we can use the most well-known form of Ohm's Law:
V=I*R
I = 25A from the BCDC regulated draw
R = The resistance in the wire + all the connections. More resistance means more voltage sag.
For the purposes of this model, I'm going to use 0.006 ohms for the resistance based on this connector designed for 30A automotive applications. It's connector type looks similar to a tow plug.
30 Amp Unassembled Red/Black Anderson Powerpole Connectors - https://powerwerx.com/anderson-powerpole-connectors-30amp-unassembled
Note that if you do a quick google search, it's not hard to find claims that the connection of a trailer plug is anywhere from 0.3ohms to 3ohms! The very small resistances are tough to measure with handheld meters because they have an extremely small test current and the resistance is dominated by tiny, needle-like probes. Yes, even you, Fluke. When attempting to measure small resistances with a handheld meter, the measurements have to be taken with a grain of salt. To measure small resistances well, one would need to send a larger, known current through the connection and measure the voltage drop.
I'll put in 0.006 ohms for the connection at the tow plug and another 0.006 ohms for the connection at the BCDC. Note, the BCDC comes with fantastic crimp connectors, so the 0.006 ohms is being modeled high.
For these purposes, I'll assume the battery charger wouldn't live on your bumper or the trailer tongue, so We'll re-use the 0.033 ohms for the 21 feet of wire from the calculations on the previous "directly wired" setup.
R = wire resistance + plug connector resistance + BCDC crimp resistance = 0.033 + 0.1 + 0.1
So back to our voltage drop equation:
V = I*R
V = 25*(0.033 + 0.006 + 0.006)
V = 1.125 volts dropped across a good clean connection ignoring any other connections that may exist on the cruiser between the tow plug and the alternator.
Let's say our temperature-compensating alternator has dropped to 13.2 volts (lowest I've measured) and we subtract the 1.125 volts from the resistive losses. That means the BCDC would only see a voltage of 12.075.
If the "Ignition Sense" wire is left unconnected, the BDCD unit would turn itself off every 100 seconds. It will check the input voltage every 100 seconds, and since 12.075 is less than 12.7 volts, it will shut itself down. And it's not even close.
View attachment 3377503
However, the BCDC (and other DC-DC chargers) have an ignition sense wire, just for this scenario! To start, let's be lazy and connect the ignition sense wire to the 12AWG wire that's carrying power to the BCDC. The threshold for the ignition sense input is 12V. Since 12.075 volts is just barely above 12, if there are higher resistances that we've not accounted for in our model, the trigger would fail. I don't like those odds.
Better would be to run the Ignition Sense wire to an ignition-switched circuit in the vehicle like here (Thanks TeCKis):
Switch Panel / Switchpros Install Underhood Tap Points - https://forum.ih8mud.com/threads/switch-panel-switchpros-install-underhood-tap-points.1217437/
At which point, yes! You can charge your trailer battery from the trailer plug! The downside is you're losing 1.125V*25A = 28watts to heat up that wire and the connectors. Not a big deal, but not ideal to have ~10% losses.
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Let's examine the thicker wire.
View attachment 3377513
We're now losing (0.006+0.006+.013)*25^2 = 15.6 watts to resistive losses in the wiring, so about twice the efficiency of using the trailer plug wiring. There are still losses in the DC-DC conversion that should be equivalent between the two methods.
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So yes, you can charge your trailer battery from the tow plug. You'd need to run an Ignition Sense wire somewhere in the truck and run that alongside your tow plug on the vehicle and the corresponding wire/connector on the trailer.
And yes, you can run a thicker wire and gain some efficiency, but 15 watts isn't material in the scheme of things. Adds more cost and failure points. The wire routing on the Cruiser is already fused, and mounted in places where it won't rub, get water logged, etc. The pins at the tow plug are serviceable. For these reasons, I'd personally lean toward using the tow plug. I didn't actually expect to come to this conclusion at the start of the analysis!
You could also mount the DC-DC under the hood to save on having to run the ignition sense wire but it's not recommended. The losses will be the same as above, just downstream of the DC-DC charger. The voltage will sag at the trailer battery during high current. Once the battery starts to fill up, and current reduces, the voltage sagging will reduce. But Redarc still doesn't recommend it.
Thank you for coming to my TED talk.