The Australian-based Scot carded an eight under par 64 at Portlethen to finish the 36-hole qualifier tied with Duff House Royal’s Callum Bruce and Portlethen’s Ben Murray on nine under par 134.
Bruce shot a 65 at Portlethen while Murray travelled to Murcar Links where he carded a two under par 69.
On another day of low scoring which started with a lengthy weather delay caused by thunder and lightning in the Aberdeen area, the experienced Scott Crichton from Leven Links carded a level par 71 at Murcar Links in the company of Murray to claim a share of fourth place alongside Blairgowrie’s Cormac Sharpe on seven under par 136.
Sharpe was also at Murcar Links where he returned a one under par 70.
Eric McIntosh from Bruntsfield Links might also be another player to keep an eye on when the matchplay stages get underway. He won the 2016 Scottish Boys’ Championship at Murcar Links and he carded a 67 at Portlethen to climb into a share of sixth place with first-round leader Steven Stewart (Clydebank & District), Craig Leith (Royal Aberdeen), Calum Scott (Nairn) and Stuart Easton (Irvine) on six under par 137.
Stewart added a three over par 74 at Murcar to his nine under par 63 at Portlethen the previous day.
There was also a distinguished group on five under par 138 with Scottish internationals Rory Franssen (Auchterarder) and Darren Howie (Peebles) both shooting sub-70 rounds at Portlethen to share 11th place with Matthew Wilson (Forres) and Scott McPherson (Bothwell Castle).
Greer plays out of the Joondalup Golf Club in Western Australia but has been a regular visitor to Scotland over the years and on his last visit to his homeland two years ago reached the last 16 of the Scottish Amateur at Crail.
He will now be looking to go even deeper into the draw after two excellent days in Aberdeenshire.
San Diego State University graduate Bruce had been tied for 26th place after steady opening 69 at Murcar Links but moved up into a share of first place after shooting eight
birdies at Portlethen. His one dropped shot at the 11th was his only blemish over his 36 holes.
Murray shot a seven under par 65 over his home course at Portlethen and he followed that up with a solid round at Murcar Links in which he birdied the first, the eighth, the 14th and 18th but dropped two shots to par on the par three fifth.
Defending champion George Burns is safely through to the matchplay stage after adding a two over par 73 at Murcar Links to the five under par 67 he scored at Portlethen the day before. His three under par aggregate was enough to see him claim a share of 23rd place.
The cut came at one over par with 64 players progressing to the knock-out competition. One of those who missed out was 2016 champion George Duncan from Windyhill who carded a triple bogey and a double bogey in a 76 at Murcar Links to miss out by two shots.