Mr Hamilton recalled being invited during his time in Berlin by the British ambassador to an official dinner during Queen Elizabeth's state visit to Germany.
"It was a grand occasion, but it came as a shock to me to realise that here was my head of state in Berlin and she was completely unable to fulfil a key part of the role required of her - to represent in this case New Zealand's interests in Germany.
On Thursday, former Prime Minister Helen Clark said it would become increasingly "quaint" for New Zealand not to have its own head of state.
Now head of the United Nations Development Programme, Helen Clark made her comments after meeting Prince Charles to discuss sustainable development issues.
She said that at some point New Zealand would have a serious conversation about the issue.
The monarchy has had a resurgence in popularity in New Zealand, largely driven by the marriage of the Duke and Duchess of Cambridge and the birth of their son George.
A Herald-DigiPoll survey in September showed fewer than one in three New Zealanders wanted to abandon the monarchy.
But Mr Hamilton makes his case for a New Zealand head of state on practical reasons as much as the more common national identity argument.
While New Zealand's Governor-General can make official visits overseas, Mr Hamilton said, there was considerable international confusion on the role and status of the position.
"I can think of one European country which has a monarch as head of state which will never receive our Governor-General as equivalent to their monarch, because they know our actual head of state resides not too far away across the Channel."
Saying "who cares?" missed the huge effect such visits could have on opening doors for New Zealand business, supporting international negotiations and campaigns and advancing the nation's economic interests.
Mr Hamilton said he found people in Asia, the Middle East and Europe particularly confused about New Zealand's international persona.
Who might be our head of state would be a decision for all New Zealanders, but the transition should happen gradually, he said.
A simple first step would be to keep the system used to appoint the Governor-General but without reference to the Queen.
Mr Hamilton said New Zealand would not have to leave the Commonwealth, and royal visits could continue under that relationship.
Monarchy NZ chairman Sean Palmer said it was a great advantage to have both the Queen and the Governor-General able to represent New Zealand. If other countries did not understand that arrangement, the onus was on New Zealand to explain it.
"The diplomatic world is all about understanding differences between countries.
"If we make it clear how the Governor-General is to be treated, then we have a great advantage."
Who's in charge?
• Each nation appoints or elects a person as its head of state. This office represents the state's historical claim to power and legitimacy.
• New Zealand's head of state is Queen Elizabeth II, who lives in Great Britain. Under constitutional arrangements, New Zealand's head of state must be a member of the British royal family.
• The Governor-General is appointed on the recommendation of the Prime Minister to serve as the representative of the Queen.
• New Zealand's head of state is non-partisan, and is not involved in the "business" of government.
• This arrangement has been described as "while the sovereign reigns, the government rules".
Read also: Peter Hamilton's full speech here.
