Sorry to break it to you, but you - as a customer - have absolutely zero right to ask for an employee's personal information let alone their cell phone number.
Unfortunately for our OP, that's exactly the type of customer
they were dealing with. Thankfully enough, the OP refused to give out any personal information (especially seeing as how the request was for a co-worker's phone number.)
This wild and crazy tale comes to us from none other than Malicious Compliance
on Reddit. The OP states that a new worker had recently started at their company and needed to leave early to meet a client. After receiving a phone call from the West Coast (3 hour time difference) the OP explained the situation to the customer on the phone. It was well past 5pm on the East Coast, and that the customer would need to call back the next day. As you can imagine, madness ensues, our OP complies (maliciously of course) and karma works its magic. Enjoy.