First, I have 40+ years as a mechanic type person who is used to getting his hands dirty. I don't wear gloves unless (a) it is very cold and I must work outside (b) to prevent blisters while using yard tools, etc. (c) dump station duties or handling chemicals.
However, I have started keeping a pair of gloves in the bag with the tow bar stuff and wear them during connecting, disconnecting. After everything is installed or removed, (including PAT) I throw the gloves back in the bag. Simple solution. YRMV