I plugged in a brand new Warm N Safe jacket into the 12 V socket accessory port, and it doesn't seem to be working. Is it possible that I blew a fuse somewhere? I looked at the riders manual which lists the fuses, but none of them mentioned the 12 V socket. As I've never used the jacket, it's possible that the problem lies in the controller rather than the socket, but before I attempt to wire it directly to the battery, I figured I should ask if there was an easy reset of the 12V socket first.
C 400 GT owner here -- not CE-04 -- but I think it's likely that you blew a fuse.
It's been my experience over the years that most heated liners draw from 7 - 10 amps, so you're probably pretty close to the max fuse values, especially considering whatever else that circuit was powering at the time. I'm basing this on motorcycle OEM fuses and wiring in general, and my GT in terms of recent Beemers. That is, my '22 GT owner's manual lists fuse values at 4A or 7.5A (except for the main 30A fuse); if the CE-04 is like that, you're over one size of fuse and, at best, mighty close to the other. (I also find that manual deficient, in that it doesn't list all the stock circuits, in terms of what fuse goes to what circuit. For instance, the USB ports in the cubby are not listed.)
So there's that.
Most fuses have two tiny openings for a pointy probe in the back side of them, so you can stick the probe from a voltmeter or a test light (with the other lead or clip properly grounded) in those tiny backside holes. That is, you can test fuses pretty easily, without even removing them. You'll have to check the owner's manual, of course, if you don't know where the fuses are.
So I'd go with a direct hookup to a battery, using, say, 14- or 16-gauge wire and a 15-amp fuse on the hot side.
And I prefer BMW/DIN/Hella/Powerlet outlets, compared to SAE or coax connectors. On two Burgman 650s and one Victory bagger, I located this outlet under my left thigh, as I think that's the best place (given that liner hookups are almost always at the bottom of the left side). Here's the sub-gallery I did regarding this mod for the Vic community back then:
And then, a few weeks after I got my new GT this past June, I did the exact same thing to that, as shown in this particular pic/caption in my gallery:
Good luck tracking down your problem.