Gemini uses multiple sets of locations, and it makes all the difference in the world when you ask if 'G2 has no clue as to it's location' what you actually mean by location.
1. Gemini mount itself is located somewhere in the world. Latitude and Longitude coordinates must be supplied to Gemini for this to work. A GPS unit can help here as well.
2. Gemini two physical axis rotate. All goto's, slews, etc. change the physical position of the axis. This is internally tracked by Gemini as the number of encoder ticks from the CWD position. This is important as without this, Gemini will have no clue where the axis are in your 'ground' coordinates or even how to get back to CWD position for parking.
3. Correct time. Gemini must know the correct time in order to know how to find objects in the sky. This can be set from PC, GPS, entered manually, or computed internally by Gemini when you start building a pointing model.
4. Gemini axis and your telescope point to a sky location, measured in RA/DEC coordinates. This is ultimately the coordinates you, as an observer, care about the most.
To allow Gemini to compute RA/DEC correctly, all of the coordinates above must be known. In addition, for accurately executing Goto's, Gemini must know how far off your RA axis in relation to the pole. This is where the pointing model comes in. It helps to compute and to compensate for the polar alignment error, as well as some imperfections in the mount itself that might affect pointing accuracy.
When you cold start Gemini in CWD position, with approximate polar alignment, with the correct geo location and time entered, Gemini knows where in the sky it's pointing as best as the accuracy of all of these values allow.
This is why the first goto is usually a bit off: one or more of the above values are not exactly right. Polar alignment may not be perfect. Time may not be exact. Your CWD position might not be exact.
But, once you do a first Align/Sync on a bright star, these variables are re-computed and stored for the next goto. Time is recomputed. Errors in CWD position are accounted for.
The next few Aligns start to compensate for other errors, such as the one in polar alignment. This is done by measuring the apparent star position and comparing it to the actual. As you add more stars to the alignment model, other mount errors are being measured and included in the computation, so that Gemini can compensate for them when doing Goto's.
There is no compass in Gemini, but there is a lot of intelligence to allow Gemini to figure out where the scope is pointing, and to do so accurately.