So been 15 hours since fridge restarted post "right-ended"
This is the Fridge Temp ...

Looks spot on.
The setting on the control panel is right in the middle (3 bars). The ripple that starts from around 23:00 is the power cycling of the AC input. So there is some kind of control going on.
And the Freezer Section
Nice consistant temp there once initially cooled down. Same ripple for same reason of course.
These Temp Sensors I have to say are brilliant

And as a Brucie Bonus, they have a feature which turns out to be excellent for this kind of monitoring.
Right now I am monitoring the power via Victrons VRM Portal. I can do the same when I switch to 12V for testing. But when it comes to checking on LPG, VRM is no use. But these Sensors don't just log temperature, they log humidity also.
In the fridge, when the cooling is active, the water is drawn out the air and settles on the cooling fins inside the fridge body as frost and ice, lowering the humidity. When the cooling stops, the fins gradually warm and water is 'released' making the air more humid.
This is the full screen in the Sensor App.
And Here is a zoom-in with the power use added on the same time line

What this means is that you can get a good idea from the Humidity chart if there is active (i.e. Powered) cooling going on or not, and this will be true of Gas as well as Electricity.
In the case of my fridge, there is no pilot light - on Gas, when there is a cooling demand the gas will ignite and then turn off when demand is removed, just like the Electric cycling.
Well that is how it is meant to work I believe

the Humidity graph will confirm that I guess
Well you did say never say never

They are good bits of kit but very heavy on electricity.
A few hundred grammes of gas per day isn't too bad and goes a long way towards balancing the cost of a purpose made 12v compressor fridge.
But if you've already got the electrical capability to support it a sub £300 domestic fridge freezer does make sense long term.
It works out in this instance to be 25 Minutes on, 15 minutes off, so just over a 60:40 on/off cycle making the average power use 137Wh/Hr. Even with this power cycling, the daily power consumption on AC is 3.3kWh.
(In terms of the Energy Efficiency labels you see on Applicances, the 94L compressor fridge I have installed as a temporary measure quotes 84kWh/Annum. This 3-Way would be 1,200kWh/Annum!)
So I am seeing a calculated average of around 3.3kWh/24Hrs on AC. There is no doors being opened to take out/out in food, so the likely consumption would be greater.
The Manual for my N180 Model states a consumption of 3.7kWh/24 Hours, so what I am seeing I think it pretty well on the money (which is good as it would confirm it is working correctly on AC). The Manual quotes a GAS consumption of 400gr/24Hours. There is close enough 2L of gas per 1Kg, so call that 0.8L LPG
Doing the maths, 3.7kWh = 62.9p (@17p/kWh); 0.8L of LPG = 54p for Refillable @68p/L (what I pay) or £1.23 for Calor (13Kg Refill @ £40)
A mid-size (150L or so) Compressor Fridge/Freezer you could expect to use 500Wh/24 hours, costing 8.5p to run - If you were to plug in your Motorhome fridge at home 24/7 for a year whenever you are not using it, the 3-Way would for a full year cost just under £200 MORE to run (£229 vs £31)
Cost of a 3-Way for a wild-camper using Calor .... £1.15 extra a day; Using LPG .... 60p more a day. Useful to know to consider if fitting a refillable would actually save money including the kit itself.