Compensation for on-call employees

Looking for advice on how to compensate employees who monitor the after hours emergency maintenance phone. I currently have a full time maintenance supervisor who works 40 hours a week. We have a call service, but if a tenant calls with an urgent issue the call service is instructed to call him. Likewise, if a vendor needs approval on a repair after hours they are instructed to call him. We can’t afford to pay him overtime pay if he isn’t able to bill the client for it, and I don’t think simply answering the odd phone call after hours can be billed to a client. If he’s called out to a billable job, sure. But otherwise I’m not sure how to arrange this. Any suggestions from other property managers?