Yea, as patrolling along the river road, if the route, would be a waste of resources. Been a while, but as you say, very little traffic.
Yes, it can depend on the route, road class and how busy it is. For example, on Highway 7 coming from Bangkok, you can see up to half-a-dozen police highway patrol cars.
...all parked up at their office where the #7 spur meets Sukhumvit in Pattaya.