In the GPS Preferences dialog, GPS tab, set Protocol to TSIP.
Set the port to COM3...that is usually the internal antenna on the GeoExplorers. It will probably be described as TSIP Serial Port.
If you have Trimble Terrasync software, you can look at its settings to verify that COM3 is the internal antenna.
When you plug your external antenna into the GeoExplorer, the external antenna is used and the internal antenna is ignored.
ArcPad will give you an estimated accuracy in the GPS Position Window dialog. Go to the Quality tab.
The Zephyr antenna may give you slightly better accuracy over the internal antenna.
There is an antenna height setting in the GPS Preferences dialog.