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The lever is located on the right side of the hammer, at the 'right' end of the manual safety body, so using the right side decocking lever closest to the sear release lever offers a bit more of a direct mechanical advantage than using the left side lever. The normal looseness of tolerances between the manual safety body and the slide, and then the slide and frame, can sometimes allow for less pressure on the right end of the manual safety body - when pushing downward on the top of the sear release lever. So can upward or downward pressure on the slide (which naturally lifts or lowers the manual safety body in relation to the top of the sear release lever)....
I meant to add that as the sear release lever approaches the worn down end of its service life, that it may be noticeable that normal decocking may not occur when the left side safety lever is depressed, but it may when the right side lever is used (more pressure acting on the right end of the manual safety body, above the sear release lever).
When a new sear release is being filed/fitted, the decocking "timing" is checked using the safety lever on the left.
Armorers used to be taught to "eyeball" the lowering of the left side lever and the decocking of the hammer, looking for the right "timing". Several years ago they started teaching armorers to use a set of 3 numbered metal drill bits, using the non-cutting ends as Go/No-Go "gages". This makes for an easier and more uniform way for armorers to check the "timing".
Also, the older sear release levers were typically machined overly long, and it could take a lot of filing and checking. This was needed on the older guns that had looser tolerances. It's easier than you might think to over-file a lever with just 1 too many file strokes.
The current levers are made to closer tolerances which still ought to work in both older and newer guns, but which often take less filing.
Before a new lever is filed, it's still necessary to check the timing and make sure a particular new lever is actually long enough to be fitted to work in a particular gun. 1 of the drill bit "gages" lets the armorer check a new prospective lever for that tolerance, before even trying to start filing/fitting it.
Getting the "timing" within the correct range is very important to the safe operation of a S&W TDA pistol. You do NOT want the hammer to start falling before the manual safety body has been rotated enough to properly capture "shoulders" of the firing pin, and rotate to cover the back of the firing pin, even though there's also a FP safety lever/plunger connected to the trigger (via the drawbar).
Even though it's a relatively simple repair for a tech, armorer or smith familiar with S&W TDA guns, it isn't a kitchen table hobbyist "check" and repair job.