Regarding where to put your off-hand when shooting Bullseye, (then) Captain Charles Askins, Jr., an accomplished Bullseye shooter if there ever was one, had this to say in his book The Art of Handgun Shooting (first published in 1939):
"...Shove the left hand in front trousers pocket, do not place it on the hip. When the left arm is stiffly bent akimbo and the hand is drapped on the hip the left shoulder is raised slightly and immediately muscles are tensed in the arm and the shoulder. Remember! We are determined not to bring into play a single muscle not needed in actually firing the handgun..."
Another renowned Bullseye shooter, WilliamC. Joyner, in his 1973 article Fundamentals of Pistol Marksmanship advised:
"...I prefer to place my free hand in my side pocket. Some shooters, especially those with long arms, can perform best by just letting their free arm and hand hang naturally at the side. The object is to entirely forget about it. It must be relaxed and forgotten. An instructor can easily spot a student who is not relaxed by the attitude of the free arm..."
The United States Army Marksmanship Unit's Advanced Pistol Guide advocates:
"...It is necessary to properly position the non-shooting arm and hand. The non-shooting hand should be inserted into a side pocket in a relaxed manner, or you may hook the thumb over the waist belt. In relaxation of the non-shooting arm and shoulder, the non-shooting arm must not be allowed to hang loose. Any wind or recoiling of the body during firing will cause the non-shooting arm to swing, transferring that movement to the body..."
Slightly different approaches trying to accomplish the same thing it seems.