UPDATE:
I fired up the LP water heater to heat a tank of water to test and it went for 30 seconds and died. I retried and it started dying after about 5 seconds. I blew it out with compressed air and it runs normally now.
After this I tried letting the fridge do a complete 3 tries to light and fail cycle though one had taken place when I first fired it up. I disconnected shore power with the fridge off and turned it on. It went through the cycle and failed. I turned it off and on again and it fired right up on gas and I instigated a series of "connect/disconnects" from shore power checking the fridge between each connection or disconnection. It functioned perfectly.
So, despite standing there for 20 minutes or so turning on the furnace, listening to the fan for 20-30 seconds and then have it cut out, turning the furnace off for 30-60 seconds and turning it on again only to have the same thing happen I can say I have made some progress.
Where exactly is the jets for the furnace? I'm getting confused. Last year the furnace wouldn't light, I blew out what I thought to be the furnace jets and it worked straight away. Now, having blown out the same place again with no good result I find that when the fridge started working on LP the area I thought was the furnace jets gets warm.
In the picture the jets I thought were the furnace jest are behind the panel with the red circle on it. There are the jets and a "sliding circle" where the arrow points that I have blown out both where the jets enter and through the "sliding circle". This is also the region that gets warm when the fridge is on. The contacts circled in blue give me 13.7V consistently.
Does this trigger a cause in anyone?