One needs to focus their business, and their marketing, to reach their target customers - and address their needs.

For example, "24 hr. service" makes little sense if your business focus is on tenant improvements.

If you're specialty is providing emergency generator hook-ups, then '24 hr. service' is essential.

I think we're also overlooking another aspect of the 25 hour day.
Apart from emergency repairs, there are plenty of businesses that want their maintenance or remodels done during off-peak hours. There are companies that seem to ONLY work at night .... maintaining the lighting at your local supermarket, setting up holiday displays for the big 'box marts,' etc.
There is even a role for 'night work' in tenant improvements. Working closely with a GC, the rock can be hung on Monday, you can do your work, and the painter can come in on Tuesday.

Likewise, there is a role for 24 hr service, if you also have other trade qualifications. For example - and here, be sure to comply with licensing laws - I've had a fair amount of refrigeration / air conditioning emergency calls this summer. Most of these problems have been the result of electrical issues - bad motor capacitors, stuck interlocks, etc.

Otherwise, if your business is based upon a handful of regular customers .... you better be willing and able to respond when they need you. You're the guy they are going to call.

How much to charge? Remember that there might more to the job than that one call.
If you're helping a proven customer, by turning up at 3AM Sunday, you've cemented your relationship with them. They won't even think of calling someone else for the next job.
If you've always been 'someone they can work with,' you've also closed their minds to sales pitches from your competition.

For those in the service business, where every customer is a one-off ... a high off-hour rate does help separate the real emergencies from the mundane. Ditto for routine off-hour work - the customer ought to pay for you to schedule for his convenience.

There's more to this than just convenience. I have a fairly large truck, and a decent inventory - but nearly every job still calls for a trip to the supply house. In a very real sense, your service schedule is determined by the hours you can get parts.