Broxup shot a two-under-par 69 in the morning and dipped one shot lower in the afternoon.
After being unable to capitalise on many of the birdie opportunities that he gave himself in round one, an eagle at the 17th made his lunch far more enjoyable.
He got off to a faltering start in the afternoon, making a double bogey on the third hole, a 155-yard par-3, but overcame the setback, although he also allowed further birdie chances to go unconverted.
Howley Hall’s Ben Hutchinson carried the Yorkshire flag alone into the final two rounds of the Scottish Men’s Open Stroke Play Championship at Gullane.
Hutchinson added rounds of 72 and 71 after opening with two rounds of 70 and finished in a tie for 31st.
Only 40 players made it through to the last day with the cut-off mark coming at three under par. Four of Hutchinson’s fellow White Rose competitors fell short, Malton & Norton’s David Hague by just two shots after rounds of 73 70.
England A squad member Will Whiteoak (Shipley) was two further back with 72 73, and Wheatley’s Ben Brewster (72 74) and Hull’s Steve Robins (74 72) both finished on the 146 aggregate.
Australian Cameron John won by four shots with a 15-under-par 269 tally, the highlight of his performance a third round 69. Ireland’s Stuart Grehan and Scot Grant Forrest tied for second.
Hallamshire’s Alex Fitzpatrick shot level par 72 in the first round of the Thunderbird International at Grayhawk GC in Arizona to lie in a tie for 13th place.
He was one under through 13 holes before dropping shots at both 14 and 16. A birdie at the last left him four adrift of Japan’s Hidetoshi Yoshihara and Americans Austin Eckroat and Norman Xiong, who all shot 68.