Success! The very next day, I had caught him. And this time, the trap killed him, so I didn't even have to finish him off. I will share my gopher trapping technique, in case anyone is interested.
I use the Macabee Ol' Reliable gopher trap. You will need at least two. I think they were around five dollars each at the hardware store. I had to do some serious critical thinking in order to figure out how to set them because they are not like a rat snap trap where the pin keeps the trap open. The backside of the pin actually keeps the trap open.
Click here if you are wondering how that works.
I know you need to anchor your traps or the gophers make off with them. I have no idea what they do with them once they disappear. I wasn't prepared and didn't have any twine, but I had a chewed leash. I ended up using this, and now think the extra thickness might be a good idea to dissuade the vermin from chewing the tether and still making off with the trap. Along with the tether, you also need an anchor. The very first time, I tied the leash to a long pvc pole (a jump bar, actually) but after that I switched to a base from a stick in the ground pole. That had the added benefit of doubling as a hole finder.
Rounding out your list of supplies should be a shovel, a hold finder (screwdriver) if your anchor won't do, and some gloves.
In order to trap one of the animals, you have to find an active hole. Look for one with moist dirt on the mound, with a pebbly texture. If the mound is smooth, it has been there a while and won't do. Dig up the mound. Take your hole finder and poke around on the inside of your hole until you find the 2 tunnels leaving the mound/ hole. This is the part I have the most trouble with. Sometimes I can't find the tunnels, and I have to fill the hole back in and try a different mound. I don't know if I am just defective, or if the gophers have already abandoned this section and back filled the tunnels. If you have 2 fresh mounds, you can also try digging a hole between the 2, and using the direction of the mounds to find the holes.
Once you have found the tunnels, use the hold finder to clean them out some more. Then (with your gloves on!) reach into the holes as far as you can, getting a lay of the land. I think I have an advantage here since my hands are small. I can go in pretty far and figure out where the tunnels curve.
Tie on your tether and set your traps. Carefully put them into the holes as far as you can reach. I think this is critical. Probably the closer the gopher gets to the disturbance you've created, the more cautious he will be. Since you've felt out the tunnel, you can be prepared for curves and can set it at a correct angle in the curve. Since you have 2 traps, you put one in each tunnel so you catch the gopher no mater which way he comes. Of course be sure to attach your tether to the anchor.
I then carefully back fill the hole. I feel that if you leave the entire hole open to the elements the gopher may wall off the tunnel before reaching the trap, fearing something tried to dig him out and it isn't safe anymore. I say carefully fill in the hole so the falling dirt won't set off the trap. They should be far enough down the tunnel that it isn't a problem. Then, I leave an air hole or sun hole or something of the sort to lure the gopher to his waiting doom. Who knows how many miles of tunnels they have under there. By leaving the hole exposed a bit, I think that it encourages the gopher to come investigate. He smells the fresh air or sees the light and wants to come see about fixing the problem. If you filled it in completely, it could be more than a day before he comes back to the area with the traps, then you don't know if you should move the traps because he's moved on, or if he just hasn't been back that way yet.
Traps should be checked daily and continue to monitor the area after you catch him since gophers will move into vacant tunnels.
If you were not successful and have an empty trap, reset the trap at least one more day in the same location. If you still did not catch anything, and especially if there are new mounds, move onto one of the new mounds. Be careful with your traps, because sometimes even pulling them out does not trip them. You do not want those pinchers going into your body (especially if they have left over gopher guts on them- yuck.) I recommend tripping the trap with the shovel.
Notice I didn't mention poison at all. I am afraid of poison due to the dogs. A sick, poisoned gopher could be disoriented and wander out of his tunnel and die and then get eaten by a dog, which would then poison the dog. Or, a dog could get into the stored poison. It is just not something I want to risk, so I use traps only.
As described above is the method I have perfected over the month or so and two dead gophers that resulted. Yes, not a long time of accumulated experience, and not a very high kill list, but so far my kill rate is 100%, so I must be doing something right.