The 21-year-old has been missing since the early hours of New Year’s Day, when he was captured on CCTV footage at 5.30am in the Church Heights area of Cookstown.
On Saturday, K9 Search and Rescue NI said its volunteers had completed a second day of searching for Mr Stewart.
“Our volunteers returned to Cookstown today to continue the search for Taylor Stewart,” said a spokesperson.
“Despite extensive efforts, Taylor sadly remains missing. We are asking members of the local community to please remain vigilant and to check any buildings, sheds, or outbuildings on your property.
“Any information, no matter how small or insignificant it may seem, could be vital and should be passed to the police as soon as possible. Your continued support and assistance are greatly appreciated as the search continues.
“We will return again tomorrow.”
It comes after the PSNI on Friday released CCTV footage of Mr Stewart in a renewed appeal for information on his whereabouts.
Local policing Inspector Wilson said: “We are becoming increasingly concerned for Taylor’s welfare and the community will see on the ground as we continue to conduct our enquiries.
“We now believe Taylor was wearing blue jeans with a brown belt, a long sleeved white shirt with a red square pattern, and green/brown boots. He is approximately 5ft 8in tall, of medium build with dark hair and brown eyes.
“We thank everyone who has come forward with information so far, and we now want to appeal directly to anyone who may have been out and about in the area at the time Taylor was last seen. Taxi drivers, for example, may have still been transporting New Year’s Eve revellers.
“If you recognise Taylor from this image, please make contact with us. Even a seemingly insignificant piece of information could help.
“We would also ask that anyone with dashcam, CCTV or a doorbell camera check their footage, and that key-holders check their premises.
K9 Search and Rescue team members looking for Mr Stewart
Snow and ice land in Belfast
“We know that some buildings may be closed to the public for the holiday season, and Taylor may have sought shelter from the current freezing conditions.
“Additionally, if you have an outbuilding, garage or shed at your home, please ensure that Taylor has not made his way inside. Anyone with information should contact police immediately on 101, or 999 in an emergency. The reference number to quote is 1108 of 01/01/26.
“You can also submit a report or information online using the non-emergency reporting form via www.psni.police.uk/makeareport or contact Crimestoppers anonymously on 0800 555 111 or online at www.crimestoppers-uk.org/.”