Hi Larry,
If you are using the (superb) Gemini ASCOM driver, to connect to your G11 then there is no need to re-calibrate when you switch imaging targets. PHD2 will adjust guiding automatically to compensate for the declination of the target.
On the other hand if you are using the ST4 guide port to guide, then yes, you will need to re-calibrate when you switch targets. I'd recommend switching to ASCOM if possible.
Calibrate PHD2 once near the equator/meridian intersection and select the option in PHD2 to automatically restore calibration. No need to re-calibrate unless you change your guider configuration or rotate your guide camera.
PHD2 calibration measures just two things: which direction a guide star moves on the guide camera chip in response to RA and Dec guide pulses, and how far it moves for a given guide pulse. If you keep your guide camera angle the same (or close, within a couple degrees) from night to night then re-running the calibration is not necessary.
Andy