First, clean and wash the 4 goose breasts (be sure to get out any steel shot pellets). Cut into Jerky strips about a 1/4 inch thick. Be consistent with the thickness. Place in a glass storage bowl and add the minced garlic, ginger, beer and teriyaki sauce. Mix the marinade and let sit in the refrigerator for at least 12 hours, up to 48 hours. Remove the goose jerky from the marinade and place on a paper towel; let dry for 30 minutes. During this time, start up you charcoal smoker. You only need 8 to 10 charcoal briquettes. (I have made this in an electric smoker but a charcoal smoker works better.) While the charcoal is heating up, mix the remaining dry rub ingredients in a small glass bowl. Place the jerky strips on the smoker rack and sprinkle the dry rub ingredients evenly over the jerky strips. Place all of your smoker trays loaded with the jerky strips in the smoker.
Use mesquite wood chips that have soaked at least 2 hours. You could use another flavor if that's your preference. Place the wood chips in an aluminum pie plate or similar pan to go on the smoker grate over the charcoals. Every hour add some of the wood chips from the pan directly on the charcoal briquets to create a good steady supply of smoke. You will need to add charcoal and new soaked wood chips as needed. The entire smoking time should take between 6 to 8 hours at 150-175 degrees.
Sample a piece after 6 hours for consistency of your liking. Once it's time for the jerky to come off, remove and store in a glass storage container without the lid, until completely cooled. You can cover with a lid after 12 hours, no need to refrigerate. Enjoy, it will go quickly.