In a search of Golf Illustrated, American Golfer, the USGA Annual Bulletin and other sources, complicated by the fact that Robert White is a common name, some activities to consider include:
1909 USGA Bulletin cites a Robert White, of Ravisloe CC, the President of PG Manufacturing Company, a maker of golf clubs and supplies.
Alec Bauer's 1913 book, Hazards, mentions White and William Watson's work at Ravisloe CC
There were a number of articles by Robert White in American Golfer and Golf Illustrated, many discussing greenkeeping issues including:
Jan 1913: Correcting a Sever Case of Acidity
Mar 1913: Watering Greens
Feb 1914: Moving from Ravisloe to Shawnee as Greenkeeper
Aug 1918: Pres of PGA
Photo with Herbert Strong
Sep 1918: North Shore CC: Greens, Summer Troubles, Crab Grass, Grubs and Fungus
Nov 1918: Top Dressing and Compost Heap
Apr 1919: Supervised Travis changes to Columbia CC
1922: Pro at Wykagyl CC
July 1924: Planning and constructing of Wolf Hollow CC
Oct 1925: Course Listing: Echo Lake CC, Longue Vue C, Greenbrook CC, Manasquan River GC, Wolf Hollow CC, Shorehaven CC
1925: Pro at Connaught GC
1926: Greenkeeper at St. Andrews GC
Dec 1928: 1st 18 hole (grass greens) course in Myrtle Beach: Ocean Forest CC
1931: Resident Secretary at Ocean Forest CC
1932: GCA office in Mt. Vernon, NY