In my first posting here, I indicated that enabling the 2 second timer automatically disables (turns off) the SR (Shake Reduction) or image stabilization. However, I went on to say that you may want to turn it back on (in certain cases). For instance, in the case of wind induced vibration of the tripod, you may want to have SR active - so as to counter this. Also, with the plastic and aluminum tripods, they may help with the very large perturbations, but leave the small ones. So, possibly having the SR on may indeed help in some circumstances - only you can decide.
The reason I post this, was when I had my old tripod, I believe that leaving SR on was actually helping, however with my newer, stiffer tripod I turn it off. I came across this example, that did a test with positive results. You need to scroll down a bit to get to the stabilization test.
VELBON MAXi 343E Tripod - photo.net
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To somewhat add to the discussion here, I had a somewhat similar problem. I was dealing with boats in a harbor (appeared to not be moving - water surface as smooth as glass - but they were), and an overfocusing problem (set the lens to infinity, but it was slightly beyond infinity - hence the DOF and hyperfocal focusing method).
Image Stabilization and Light Weight Tripods - Steve's Digicams Forums https://www.pentaxforums.com/forums/general-photography-techniques-styles/653...otography.html