In a sitting position, pushing down on the body, resting my right arm.Not sure what you mean by putting pressure to the lower part of the guitar. Are you pushing or pulling the neck back or forwards?
OK, so you are holding the neck while you do this. This would tend to bend the whole thing slightly. SGs are particularly bendy guitars. This is really easy to do. There's nothing wrong with it - just practice not leaning too hard with your arm.
Welcome, by the way.
I've been doing the "SG Shake" for decades and never had a neck joint fail from it.
I don't go crazy etc, but much like Brittany from Alabama Shakes, just gently rock it back and forth.
'61 RI...
IMHO those are one of the best guitars ever made.