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Basically replace it with an old school friction shifter.
Thanks, it wouldn’t have crossed my mind to do that!The SA and SACHS/SRAM 3-speed shifters, are properly indexed for the 3-speed SA hub. Purely friction shifters can be used, according to the Sheldon Brown technical website, but then you have to memorise the orientation of the shifter when selecting the middle gear --- apparently, it was when it pointed at his navel...
Basically replace it with an old school friction shifter.
Thanks, it wouldn’t have crossed my mind to do that!