The British 25-year-old failed to return from a day trip to climb Mitre Peak, in Milford Sound, last Sunday, and police have been combing the area for him for the past week.
In the past few days, a light was spotted near where he went missing, and the search has been focused there.
Wilsons Abel Tasman chief executive officer Darryl Wilson, of Nelson, said Eli had been working for him on one of his cruise boats, from December last year until last month, and described him as "the life and soul of the party".
"He was great with customers, a very outgoing individual, and he was a credit to himself, our organisation and his family.
"He’s the kind of guy that can make friends with anyone, and there’s never a dull moment when he is around.
"He’s the life and soul of the party. He had quite a nice night on the dance floor, the last time I saw him on it."
Mr Wilson said he and his staff were extremely worried about Eli.
"At the moment, there's a lot of grief, a lot of tension, and a lot of emotions running very raw.
"So we are obviously all very torn, and we’re wishing for a positive outcome.
"We’re waiting with bated breath."
Eli’s 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. —Additional reporting RNZ
