I worked a night shift for 2 years in Houston, on call from 2-5pm (whenever) to 5am, and every other weekend was on call 24 hours, and I was given calls as far as 150 miles away, for which I would use my car. Apparently they had expected me to use my car for all of my calls, instead I did anything inside the 610 Loop on a bike.
But I was the only one, Jess would help until midnight sometimes, no other bikers worked after 7pm unless working late at a courthouse or library. The night rates were great, even short, one zone dt to dt deliveries paid 3x & 4x the daily rate, depending on the client anywhere from $20 to $45 per call. This was at a high end messenger company w/good wealthy clients
It's a peaceful time to ride, between 3 & 5am, it's easy to remain vigilant with traffic when the only thing out there are cops & drunks.. But long on call stuff like that is only good for single people.
Most 24-7 delivery agencies I've worked with turned all dispatch over to a night driver who would double as dispatch & run just 2-3 vehicles, even at a large company running 20 bikes & 50 cars during the day.