RM 9616I-LM Antenna

The 'GPS' aerial is not part of the power cord, the unit functions with no power cord pugged in when the internal battery is sufficiently charged, so it can't use any external cabling as an antenna

The 9616 does not have a socket for an external antenna and can not use one

 

A GPS antenna is usually a ceramic square like this



It is typically 10 - 20 mm square and in this case is almost definitely positioned on the main printed circuit board inside the unit, it could be badly soldered to the main board, but I think that is unlikely unless the unit has been dropped, however there are other causes of GPSs failing, for example, the unit has an internal 'clock' that needs to be very accurate, if this clock is too far out the unit will have difficulty getting a satellite 'fix'

As you say, your position on earth shouldn't matter to the GPS, as every part of the globe is covered, although above 60 degrees North and South the signals are reduced, things that can effect a 'fix' are, things that get in the way such as tree cover, the metal in a car, buildings etc. so try it out of the car in an area with a clear view of the sky. If you find it it always works better when the temperature is above or below average, that might suggest a problem with it's internal clock, because it will vary with temperature

 

You wont be able to see the error, we are not talking Seconds, we are talking micro / nano seconds, the unit has a quartz crystal (like in a watch), that drives the clock, but it needs to be within a few parts per million to work, as I said above the crystal is affected by temperature