Well, the best way I know how to do it and pretty cheap, too ... is to get your shovel out “dig it up” in that spot. It shouldn’t be too hard. I had to do that myself a few months ago and found the broken spot, right where it was apparently real moist.
Just consider it exercise and it’s for free ... Otherwise, if money is no object, just call the plumber... :-)
Beat me to it! If you get down 18"-24" and the soil is or isn't significantly moister, you'll have an answer.
Besides, if it was a small sewage leak , it'd make the grass greener, not kill it off. If it were a large sewage leak, you'd know it.