I'd have to check on the boat for the wire size; all wires are speced for less than 3% drop at the maximum circuit draw, probably 12-14 AWG in this case. Since this happens when the device is on standby, I tend to think that's not the issue. However, you're right that it might be very reasonable to double-check; I will do this the next time I'm at the boat.
Some of your symptoms sounded like it may be due to a power issue, I could be wrong, of course, but that would be the first thing I'd check.
I'm not sure about your specific model, but I was mildly annoyed when I bought a larger gauge wire for mine (I had to run a pretty good distance), only to find the adapter wouldn't fit the larger wire.
By jog, I mean manually extend or retract the tiller using the control head. The manual says not to force the ram in or out, and the dealer said that there is no clutch that can be disengaged in standby. That poses a problem when trying to engage the autopilot, since the length of the arm generally is not correct when I need to physically place it on the tiller pin. So what I have to do is steer way off course until the tiller is in the right place, then put the autopilot on, and then hit 'Auto' and hope the pilot corrects before I slam into the bulk freighter docked at the edge of the channel.
I am glad that I'm not the only one that hasn't figured this out yet. Granted, I haven't had an opportunity with enough space to really try and figure it out, but I'm gonna make a point of it next time we go out.
I've had mixed luck getting it on, about half the time it goes on and keeps the course just fine from the start, the other half I end up swerving everywhere until I get it setup. There has to be a better way...