The pensioner's death notice said he was a loved father and father-in-law and a grandfather of six.
Director-general of health Ashley Bloomfield said at the time Brookland had been diagnosed with Covid-19, but was not "clinically unwell" before his death.
He had been being looked after at home by family and was subject to "daily check-ins" by health officials.
Dr Bloomfield said it took several days to link the case to Covid-19 because "the circumstances around that person's passing were such that we felt it important to get a really good understanding".
"That can help inform our knowledge base around how we manage people in the community with Covid-19, particularly if they have pre-existing respiratory conditions."
Asked whether Brookland should have been in hospital, Dr Bloomfield said the case would be reviewed by chief science adviser Ian Towns, a respiratory physician, and some of his colleagues to "look at what the learnings are".
SDHB chief medical officer Nigel Millar said the death was recorded as an adverse event because the death was unexpected.
"At the time of this tragic death we were still in the early stages of learning about this disease."
The health board needed to learn from its response to Covid-19 and the death had been recorded as an adverse event to ensure the DHB knew as much as it could about what happened.
Finding out how it came to be that Brookland died at home would help the board understand whether his death was avoidable and whether there were things it could do in the future to avoid a similar event, Millar said.
It was not clear from his response what stage the health board's investigation was at or whether any changes to policy had been made at the time or since.
Brookland's family declined to comment.
