This is all new for me too, came from a small city lot 7 months ago and moved to gopher central. I put my roses, daylilies and a few special plants in gopher cages to protect the roots.
One day one of the big dogs started digging and exposed a hole in the lawn, I pulled her away and leaning down, I could hear the gopher digging so realized it was quite near the surface. I was watering so stuck my hose in the hole and held it there and all of a sudden, the gopher started pushing up against it trying to get out. I kept the hose there for at least another minute and when I pulled the hose out, it flopped out onto the lawn, it had drowned.