The British man failed to return from a day trip to climb Mitre Peak on Sunday.
The search was called off on Thursday because of bad weather, but police said their efforts would resume on Friday, with fine conditions forecast.
His family has flown in to help with the search and appealed for help and donations on a GoFundMe page which shared a statement from his sister Serena Sweeney.
Serena noted the "incredible effort" by police, search and rescue teams and Milford Sound locals.
"There has been a light spotted at a point along the route down the mountain and all efforts have been focused there."
The bush in the area was so dense that it was hard for infrared to pick up any signs of her brother.
"We need more people on the ground but this has to be experienced climbers who can safely belay themselves in and out of the area."
She described her brother as "one of the kindest, most compassionate people" in her life.
"He inspires me to live and get out of my comfort zone, as well as listens and genuinely wants to know you and your story.
"Anyone who has met him will know what I mean. He has such a positive, vibrant and supportive energy."
The fundraising effort aimed to support the search for Eli as well as raising money for local search and rescue organisations and Real New Zealand.
"My brother is an experienced climber and has hiked in this terrain many times. I also spend time in the mountains and know how incredible it can be up there, but how quickly things can change. It could happen to any of us."
Police said about 60 volunteers, 10 police staff and helicopter and tourism staff were involved in the search.
Surf Life Saving said personnel from Otago and Southland would join the search when it resumed. The six-member team was to search the shoreline and water with inflatable rescue boats and a jetski.
- APL/RNZ
