"If you don't want to call, write a letter and let us have the peace we need," Mrs Wilkinson said.
This week, a $25,000 reward has been posted through the Crimestoppers organisation for information that locates Mr McAllister.
"We are very fortunate that a family friend has given us this great opportunity to try and get some information about what has happened to Dad," Mrs Wilkinson said.
The person putting up the reward money wishes to remain anonymous.
Detective Paul Heathcote said Mr McAllister could have died as the result of an accident, been a victim of foul play, or could be still alive somewhere undetected.
"We have no evidence to suggest one theory over another. However, logic obviously comes into play and the longer we don't hear from Hugh, or hear about him, the chances of him absconding grow slimmer."
Mrs Wilkinson last saw her father a couple of days before he disappeared, when he was at his granddaughter's 18th birthday party.
"He was just the same, enjoying life, enjoying the company of family, so it would be very out of character for him to just decide he would take off," Mrs Wilkinson said.
"He had been down on the West Coast for approximately four years - like most gold miners, trying to find the big nugget. He was in good health, he liked living on the West Coast, he had made some great mates.
"As a family, you never really think something like this is going to happen to you, but it has."
* Anyone with information on Mr McAllister should contact Crimestoppers on 0800-555-111 or visit www.crimestoppers-nz.org
