Davis doesn't believe in UFOs, but he said that "she seemed like a logical person who wanted answers." Besides, he loves the challenge of working cold cases. And the nice hourly pay. So he started nosing around.
He went to the Internet, trawling for witnesses.
Some who said they saw the craft likened it to a dragonfly or an upside-down egg beater. They described it variously as an exploratory craft dispatched by a mother ship and a top-secret government project.
But in chat rooms, Davis also found plenty of drone doubters, who made comments such as "Looks like a new kind of torque wrench" and "Did you folks get a picture or two of the crop circles?"
In one exchange, when someone asked about the meaning of the writing on one of the craft's arms, the snide responses flooded in: "Made in China." "Martians for Obama."
Word of Davis' case quickly spread among his ex-cop cronies. T.K. had gone galactic, they joked at their weekly drinking sessions. He was seeing little green men. Davis let them laugh, just as they had when he'd taken a night class in meteorology and spent weeks chasing tornadoes in the Midwest.
"I'm not chasing flying saucers," he said. "I'm knocking on doors, looking for people, just like I've always done."
Then he got a call from Dixon, a fellow retiree he'd known since the two worked on a 1970s narcotics task force. Dixon, also a private eye, had heard about the case on the golf course. He wanted in. "I'm your man," he said. "I can find that pole." When Davis said yes, Dixon went out and bought a book about Roswell, N.M., the site of a notorious UFO sighting in 1947.
The pair devised a strategy: Don't buy into any far-fetched "Star Wars" theories. And don't admit the case has anything to do with possible alien spacecraft. If you start talking about flying saucers, Davis warned, people will start closing doors.
"We were working for people who didn't want to be identified," Davis said, "looking for people who didn't want to be found."
Dixon quickly became an expert on utility poles.
Like fingerprints, he says, each pole is different. Some carry only telephone wires. Others also have cable-TV hookups. Most, but not all, have short rods for climbing.
He visited the power company with one photo -- with the drone carefully edited out. He said he was working an auto accident. Could they tell him where the pole was?
He then visited the website of the Mutual UFO Network, dedicated to extraordinary sightings, where a man named Isaac claimed that strange craft resembling the one Dixon and Davis were investigating were part of a U.S. government project. Isaac said he knew this because he worked for a top-secret government program in Palo Alto in the 1980s, devising commercial technology from extraterrestrial artifacts confiscated by U.S. scientists.
Isaac wrote that he worked five stories below ground. Dixon consulted fire officials, who keep records of building heights and depths, but could find no record of such a place.
Running into such dead ends, Davis took a chance and began mentioning the real reason for his search.
Sometimes, it actually seemed to help.
"They'd call it baloney and then admit, well, maybe they had seen something funny one night in their lives," he said. "Everybody's in the closet."
One person said she'd seen the drone in Sequoia National Forest. "It was broad daylight. I was sober," she said. "I'm not known for seeing things." Dixon had his doubts, because she couldn't even recall what day it happened.
Before hiring Davis, the woman from the Open Mind Forum called Capitola police to report the photo and request an investigation. Chief Richard Ehle considered the whole matter a farce, but assigned a detective to it just in case.
Sgt. Mark Gonzales found nothing.
"We're a small beach town, and residents report everything from cat feces on lawns to sick sea gulls," he said. "If someone saw something, I'd know about it."
But he said he wouldn't immediately close the case. "I keep an open mind," he said.
So do Davis and Dixon. They recently uncovered some new leads. At a party, Davis mentioned the drone to a friend. "I thought he would have thrown me out of the room." Instead, the man offered a theory about the location of Isaac's secret Palo Alto laboratory.
Davis has started a website for tips: www.tkdavisinvestigations.com.
"The more I get into this, the more I want to know," he said. "It's weird."