A couple spotted the 30-year-old strolling through parkland at Crichton Castle at about 1.30pm on Sunday.
Mr Taylor disappeared from his Mayfield home at noon on Sunday prompting a massive police search.
“They spotted someone matching his description and they thought it was a bit strange because he was on his own and didn’t have a dog,” said chief inspector Arron Clinkscales.
Specialist search teams with police dogs and the force helicopter are now scouring the area for clues as to Mr Taylor’s whereabouts.
“We’re throwing everything at it,” said CI Clinkscales. “We won’t rest until we find him.”
Mr Taylor’s partner, Laura D’Arcy, six-month-old son Lewis, and stepchildren Liam, eight, and six-year-old Jessica are being kept informed.
“She bearing up but she’s desperate to get him back,” said CI Clinkscales.
Baby Lewis underwent extensive open heart surgery in January after being born with a serious defect.
“It’s been a stressful time for the family,” added CI Clinkscales. “Lewis wants his daddy back.”
Mr Taylor is described as white, 5ft 9ins tall, of skinny build, with short light brown hair.
He was last seen wearing grey jeans, a black jumper and blue Converse trainers with white soles.
CCTV footage captured on the home security system shows him pacing on the driveway before he vanished.
He had no cash, no phone and left his car on the drive – with concern growing as the weather deteriorates.
“He’s a loving family man and takes good care of myself and the three children – this is completely out of character,” a tearful Ms D’Arcy told a press conference this week.
She thanked the public who have joined the search which included police drones and two helicopters – including the search and rescue chopper from Prestwick.
Sixteen of Mr Taylor’s workmates at energy firm SSE are understood to have joined ever frantic efforts in their vans.
“I’d like to thank everyone who’s helped with the search – it’s been so overwhelming,” said Ms D’Arcy.
“I’ve had people coming to my door – complete strangers – offering to help. We appreciate it so much.”
Police have asked residents to check their gardens and sheds in case Mr Taylor has sought shelter.
CI Clinkscales added: “As part of our inquiries we’re asking anyone who may have seen Ross since this time, or who has possible information on his whereabouts, to contact us.”
Those with information can call Police Scotland via 101, quoting incident number 2570 of March 31, 2019.
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