If you have maint contracts to support 24/7/365 they should have customer service reps working 24/7/365 who can proccess calls, determine the level of severity, and the response time it requires contractually. Answering services can do this, contacting management level personel to determine escalation levels prior to contacting technical staff. The technical person should not be taking calls from the customer ever, nor should they be responding to the CSR/answering service, but management should be handling that, and compiling a work order, and then the manager dispatching a technical person to do only the technical work.
You do not become a CSR, operations manager, service response level decision maker, dispatcher, just because it is after hours. By the time you are involved there should be a work order, scope of work, billing rate established/communicated to the customer, and fully documented as would any in hours services required. After hours you do not simply by default do everyone elses job within your organization. After all, since it hardly ever happens that there is a call out for emergency service, these other people who normally have duties to do prior to you going out to a site should not mind having to remain available as well.
In an in house situation, that call should also go to managament first, then they respond as needed contacting technical persons if justified. Never simply having technical persons contacted directly at home by people who are not in personel, or management. There are legal issues to posting employees personal information in unsecured areas anyway, like putting peoples home phone numbers on company phone lists, etc. This is not proffessional, and can cause you legal issues, since it is the companies responsibility to keep this data confidential. There is no need for your co-workers to have your personal phone numbers, ever!
Proper business etiquette provides for HR to have your personal phone number, in some cases your direct supervisor, but these are to be kept secure, and never given out to other persons. If the company provides a cell phone, or a business line at home, then that is their business to distribute as they desire, otherwise management only.
Managers may not like this, but hey guys, step up to the plate, make the decisions, and consider the techinical person who gets no life. They already have to remain close at hand to respond for legitimate techincal issues, the least you can do is not leave your job, or anyone elses to them as well. They are not your 24/7/365 telephone receptionist, service manager, CSR, dispatcher, operations manager, service order proccessor, help desk supervisor, etc.
Try getting a bid for this support via a third party company of the quality you expect from your people. Then consider those bids, and the actual services you would farm out if you had to actually pay for them. You would probably only contract out the technician services, and handle the dispatch, etc. in house having your managers take all the emergency calls then call the third party tech with all the data compiled to communicate their scope of work. When you get that $ figure, you have an reasonable number to work from. In house you can expect to pay a little less since the third parties profit is not in there, say a % of that bid is what you should be paying your people.
Or just screw them over, whatever.