The 74-year-old was last seen at around 9am on Friday 25 October, on the walking track directly behind Harcourt Park in Upper Hutt.
"Terrence used this track often and would regularly ride his electric one wheel scooter between the duck pond through to Akatarawa Road Bridge," Detective Inspector Haley Ryan said.
"On the morning of 25 October, he had his electric one wheel scooter with him, however on this day he could have been carrying it, which would give the appearance of him carrying a black box."
"He also had distinctive red basketball boots, which he may have been wearing or also carrying."
Police have fears for Jameson's safety and are asking anyone who may have seen him on 25 October or who may have information which could help locate him to call 105 and quote file number 241025/6976.
Residents in the Harcourt Park/Brown Owl area can expect to see a continued police presence on Sunday too, as officers continue to search for him.
