Prosecutors charged Alan Kimble Fahey, a retired telephone service technician, with 14 misdemeanors.
Jurors asked that attorneys for both sides reargue their cases on the other counts so they can deliberate further. The judge agreed and told the attorneys and Fahey to return to court Wednesday morning.
If convicted of all charges, he could face as much as seven years in prison.
Los Angeles County officials said Phonehenge West, a collection of eccentric structures, is a safety hazard and must be torn down.
Supporters call it a work of folk art and compare it to the Watts Towers, which were built by another self-taught craftsman, Simon Rodia.
Fahey spent three decades building the network of colorful towers with recycled wood and equipment he collected from his jobs over the years.
The Associated Press contributed to this report.