I'm not going to look it up (will leave it to discussion here to sort it out), but iirc the fangs of a garter snake are in the back of their mouth, so you'd have a finger fully bitten, or an otherwise "full" bite to likely be affected, no?

I wouldn't call their rear teeth "fangs". I don't think they are even grooved like rear fangs. In colubrids, the venom is in their saliva, so even if you are cut by one of the front teeth, that can be enough to get envenomated. How much of a dosage you get really comes down to how much the snake "chews" on your hand, which mixes in the saliva and thus the venom.