Mine ran diagonally across the front yard from the meter out on the road to where the water entered the house. The good news is, if they are similar in differing parts of the country, it's a small, easily repaired pipe. The worst part of having it leak is not knowing where it's leaking. You won't have that problem.
I dug mine out and fixed the leak myself, and I am a little old lady.
I would do it since your meter is in back of your house and you are working in the front.
How bad do you want that fence?