Does not sound normal to me. The difference between low cool and high cool should only be the fan speed. The compressor should run the same in both cases. It sound like you may have a defective switch where the compressor is not running in the low cool position. Listen carefully and you should be able to determine if the compressor is running or not.
Chuck - Sparta, TN
2012 Jay Flight 22FB, 2 x Honda EU2000i
2013 GMC Yukon XL Denali AWD
EDUCATION is what you get when you read the fine print.....
EXPERIENCE is what you get when you don't.