According to William Pitt Chambers' journal, the 46th was positioned about 4 miles NE of Pollard, AL (that'd be near present-day Brewton) in late March 1864. In his March 23rd entry, Chambers wrote "on Friday last [March 18], Lts. Buchanan and Duckworth started home on 'unlimited detail' to collect the company." The two Lts. (with about twenty others from Company B) rejoined the command on May 26th near New Hope Church, GA.
This furlough may have allowed time for picture taking, although there were concerns at home that may have kept him there longer. The Jones County deserters (Newt Knight's band) were also causing problems in eastern Covington County, where the Duckworths lived. Mobile and Montgomery certainly could be possibilities as the regiment was run around on the rails quite a bit after the fall of Vicksburg and before the Atlanta campaign.
Thankfully, these entries from Chambers journal also explain -- reassuringly to genealogists -- how J.T.'s wife could have given birth to twins in December 1864 when her husband was presumably off to war the entire time! From Dec. 1863 on, J.T. was a second Lt.; maybe material shortages allowed him to wear a collar one step above his station for a photo taken at one of these cities....? I appreciate your comments, Alan.