The shifter rattle is most prominent above 6k rpm in third gear, so I found a place where I could go WOT in third from about 4k to redline. I also (mostly arbitrarily) chose the following three positions for the damper:
1. As far down as it would go
2. As far up as it would go before slipping off the shank
3. Roughly in the middle of the previous two positions
Most of the force that is oscillating the shift lever back and forth should be coming from the selector rod and carrier, as the rest of the points are suspended with rubber bushings. Felt to me like the selector rod would play the biggest role, so my guess was that the higher the damper sat, the more it would dampen the rattle, since more force would be needed at the selector rod joint to move the shift lever through the same angular displacement.
Testing consisted of me setting the damper to one of the heights and then doing a WOT pull. I recorded each pull with my phone (placed in the same spot) to try and quantify the rattle.
I put the audio from the three pulls through a low pass filter to isolate the rattle and then tried to match the gain across all three tracks. That last part was more of a guessing game than anything else, since I couldn't turn off the dynamic mic gain on my phone, but still good enough. Here's the spectrogram comparison with a rough rpm guide overlaid (rattle is the red areas):
The most prominent thing to note is how the amplitude of the rattle is pretty much constant all the way from 6k to 8k in the top position, grows with rpm in the bottom position, but it is really only loud from 6.5-7.2k in the middle position. Not at all what I was expecting! But my anecdotal observations do match the data. The middle position seems much better tuned.
So, turns out my hypothesis was wrong. Guess the carrier contributes more than I expected? Either way, glad I ran this experiment and learned something new.
I'm pretty sure there's more to be tuned, but I can't think of a way to do it on the street without spending hours doing the same thing with much smaller vertical displacement increments. I have been kinda wanting to go back to the dyno now that I have the wideband in my headers, so that might be the perfect opportunity to do this. Can just hold the car at 6.5kish rpm in third and move the damper up and down to find the sweet spot.
Anyway, gonna leave it in the middle position for now and maybe I'll mess with it again in the future.

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