The Brigades of Micah Jenkins and Montgomery Corse (3700 men) were detached during the Gettysburg Campaign, making Pickett's Division the smallest infantry division in Lee's Army. Corse's troops were on garrison duty in the area around Suffolk and Jenkins' men were to remain and guard Petersburg and Richmond.
Gen. Pickett Brigades marched in two lines, led by the brigades of Brig. Gen. James L. Kemper on the right and Brig. Gen. Richard B. Garnett on the left; Brig. Gen. Lewis A. Armistead's brigade followed closely behind. So I'm guessing you mean Gen. Armistead as he was the reserve
Edit - The question was about brigades that were absent from Gettysburg altogether.
Answer: Corse's Virginia Brigade and Jenkins' South Carolina Brigade.
After the Suffolk Campaign in which Pickett's Division took part, Corse's Brigade remained on garrison duty in the Suffolk area and Jenkin's Brigade was guarding Richmond and Petersburg. (Only Corse would rejoin Pickett's Division after Gettysburg while Jenkins Brigade was assigned to Hoods Division) http://battleofgettysburgbuff.com/More_Odds_and_Ends.htm (near the end of the page)
Edit - Since different sources give different locations for these brigades, I'm accepting any answers that say they were in Virginia.
Note - I still do not know who submitted this question. If you see this edit, please send me a private conversation and let me know that you submitted the question, so that I can give you the ten points credit you deserve.