Purely based on my recollections of the G&F operations in the mid-1960's, a yard, in the general image of a yard, didn't exist. The G&F had about 2 or 3 tracks that were used for all needs, such as car set outs, storage, and as team tracks. Officially, it was classified as a yard, with yard limits markers. If any switching or car movements requiring crew members on the ground occurred, rules required that a yard limit be declared for safety purposes (slow speed, clearance checks, etc.)
By the time that the Southern Rwy took over the line, one train out of Millen via Midville traveled the line to Hazelhurst and returned. This train handled all of the work on that section of the line. Another train operated north out of Langdale Yard in Valdosta to Hazelhurst and return. Cars were set out and picked up at Hazelhurst, except the cars that went back to Millen or Valdosta.
Later, NS assigned a switcher at Swainsboro for local work on the north part of the line. I believe by that time, major parts of the ex-G&F line, including the portion through Vidalia, had been placed on out of service status or abandoned. In such situations and by arrangement, other railroads would pick up the local business services where needed, such as you described in Vidalia. The same practice was used by NS in Tifton, GA when the CSX pulled off of their line between Albany and Pearson.
Wish I could be of more help. I thought that I had taken some photos in the '60's - '70's in Vidalia, but I couldn't find any record of such. Sorry!