Cigarette Lighter Plug Question

[GumbyDammit223]

I've been trying to power up my Max360 inside using the supplied cigarette lighter plug connected to a deep cycle battery I have. I'm trying to verify settings and make sure my new phone can connect to it in the relative 80° comfort of my apartment instead of a 100° car. The problem is that the plug doesn't power up with the power receptacle I've had for some 20+ years.

I don't think the plug's tip is making contact with the center button of the receptacle because the plastic tip of the plug is too large a diameter for the receptacle. Other plugs I bought at the same time as the receptacle when I made my adapters have smaller diameter tips compared to the Escort one.

Doing a quick search tells me that there are two different sizes out in the wild, and I'm guessing my power adapter is the smaller A size while the Escort plug is the larger B size. Can anyone confirm the specs of the Escort plug size?

I know the SmartCord works because I can plug it into the car's outlet and it powers up, but that's not what I'm after. Thx.