Definitely do-able and unfortunately not configurable through the local phone interface nor via the phones web interface. These will need to come from a Zoom phone template. I had it working, but kept tinkering with other settings. Finally got back to where I was in a good working state. Try the first two parameters and if it doesn't work? Add the last two to your template.
call.callWaiting.ring= "ring"
call.callWaiting.enable=" 1"
voIpProt.SIP.alertInfo.1.class= "custom1"
voIpProt.SIP.alertInfo.1.value= "custom1"