Wallace was a corporal in the Union Army during the American Civil War who acted as Angel Eyes' adjutant at the prisoner of war camp where Angel Eyes was posted after becoming a sergeant in the Union Army.
Angel Eyes was determined to find the buried Confederate gold and had Wallace call out the name "Bill Carson" during roll calls whenever fresh consignments of Confederate prisoners are brought in. Wallace was a large and powerful man and had brutally beaten up many of the prisoners in the camp on Angel Eyes' orders in order to extract information that could lead him to the gold. A band composed of Confederate prisoners was always made to play during Wallace's beatings in order to drown out the cries of pain.
Tuco Ramírez was subjected to one such beating and was forced to come out with the information that the gold was buried in Sad Hill Cemetery but he could not say where it was buried as only Blondie knew the name on the grave where it was buried. After extracting all of the information he could out of Tuco, Angel Eyes had Wallace take Tuco away to be turned in to the authorities and subsequently be executed for his crimes.
Wallace was evidently told the whole story of Tuco and Blondie's money-making scheme by Angel Eyes, as he gloated to Tuco as the train arrived in the station that there would not be any partner this time to shoot him down.
Once on board the train and handcuffed to Wallace, Tuco needed to relieve himself and Wallace stood with him at the open door of the railway wagon they traveled in. Tuco then said he could not relieve himself while Wallace was watching and Wallace looked away. This whole act was actually a ruse by Tuco to escape and he pushed Wallace out of the railway wagon and the two of them tumbled down the railway embankment together, Tuco using Wallace's body to break his fall. Wallace was out cold but Tuco then had the problem of separating himself from Wallace. Tuco tried severing the chain with stones, then with Wallace's gun which refused to fire, so he hauled Wallace up the embankment and placed him on the railway. Tuco laid on the other side of the rails and waited for a train to come. A train soon arrived and separated the chain of the handcuffs and ran over Wallace.