That really depends on location. In smaller towns, cops often sit in their vehicle at night and do absolutely nothing but wait for an infrequent car to go by. They occasionally drive around doing nothing, going from one place to another to check on pretty much nothing. Tons of downtime to think.
I've done a lot of engineering work in the manufacturing sector (both directly employed and as a consultant), and I know for a fact that most of the mechanics/machinists/electricians/operators/etc. believe that engineers do absolutely nothing all day.