I cannot fathom any current B738 driver sitting with his thumb on the pickle switch for that length of time
I have seen this happen in the simulator on a few occasions. Always during a go-around where the natural pitch up on application of GA thrust is not contained immediately. Usually this happens in IMC where no visible horizon is available to see not only the rate of pitch up but how much above the horizon. In other words poor instrument scan.
Instead of using immediate strong elevator force coupled with careful forward blips to the stab trim to contain the pitch up, the pilot uses the stabiliser trim switch in a continuous motion and keeps his thumb on the switch waiting for a reaction. 12 seconds is a long time to wait for the nose to lower and by then it goes nose down rapidly and no hope of recovery at low altitude on instruments.
It all boils down to poor instrument flying manual skills. Blame lack of proper simulator training in the manoeuvre in terms of manual go-around procedures. Auto go-arounds are a non-event. Manual go-arounds are another story altogether especially on instruments