I hooked up one of the detent potentiometers to an Arduino Nano and took some readings. I thought that with 11 positions in a range from 0 to 1023 that they would most likely be evenly spaced apart. Not so! The lowest position gives a pretty solid 0 but the next position is around 14. So I used a table of threshold values to map the readings to index values from 0 to 10 (11 distinct values).
The program (sketch) is in the attachments. Here's a run starting from the top and turning the pot CCW and then back. The index is shown first followed by the value obtained from the A/D conversion.
The sample time for the readings is set at 100 ms. And yes, you can miss a stop if you turn the pot fast enough. Once in position, the readings turn out to be pretty steady varying maybe 2 or 3 values. I'm not sure if all of them will work this well or if my table of threshold values will hold up in all cases; I arrived at the values using the GRJ method of observation.
The good news is that these will work out for what I have in mind. I mounted the pot in a plastic box and ran a 6 foot cable to the Arduino for these tests. They will be useful for controls on a front panel.