How to trace corrugated drain pipe without digging up my whole yard?
Any decent plumber with modern equipment can run a line-locating snake down from where the gutter drains into. The tip/head has an RF transmitter and the plumber walks around with a detector that tones at different pitch the closer he/she gets until they are right above it. Should cost no more than like $100 max. Save yourself some trouble and call someone in to do it.