The 21-year-old amateur champion had not even turned three when Rose, from Hook, chipped in on the 18th from 50 yards off the green to jump up the leaderboard and tie with Tiger Woods.
The Hampshire man turned professional the following week.
Ellis, the youngest player to complete the English and British amateur double, is in no hurry to join the paid ranks – but intends to savour every stroke on his Open debut.
The Meon Valley man is also expected to receive the traditional invite to play in the Masters in April as a result of his British title triumph at Royal St George’s last month.
‘I remember watching Tiger win at St Andrews on the telly in 2000 – I was five,’ said Ellis.
‘I remember a lot more of his win in 2005.’
By then, Ellis was already making a name for himself playing in the HSBC Wee Wonders, which held their finals at St Andrews.
He added: ‘Tiger was the one for me but by the time I was 13 or 14, I obviously became aware of how well Justin played at the Open at Birkdale.
‘And playing in Hampshire’s junior competitions, which he had played in at the same age, I started to realise that I could follow the same path if I was successful.
‘When I won the English Amateur in 2012, I got an exemption into the second stage of qualifying for the Open.
‘Then I realised I was just 36 holes from playing in it as an amateur – just like Justin did. I have not played with him before but he has sent me personal messages after my big wins – and after my mum died in 2013.’
Ellis arrived in Southport on Sunday, having flown into Manchester from Austria where he had helped England to silver in the European Amateur Team Championship.
He said: ‘I played 10 rounds, including practice, in seven days but I feel really good coming into this week and think it was the right thing to do.
‘I played well and feel good coming into the tournament.
‘I played nine holes with the US Open champion Brooks Koepka on Monday and found myself playing with Stewart Cink, Martin Laird and Aaron Baddeley on the back nine yesterday.
‘The great thing is I have felt really at home in their company and feel like I’m in my own little bubble already.
‘I’m confident about the challenge ahead.
‘The game feels good and while the weather forecast is not as good later in the week, the course is in fantastic condition.
‘The way I have been playing, if I can reproduce that on Thursday and Friday, I don’t think making the cut will hold too many fears for me.
‘And then I can think about giving myself the chance to be involved in the presentation ceremony on Sunday by winning the Silver Medal.’
The Silver Medal is the award given to the leading amateur in the Open’s final standings.