We are integrating using the REST api, which is working well, but I am unable to find any reference to continuous or relative motion anywhere. Does this functionality exist within the REST API?
No.
The REST API only have:
GetPtzAbsolutePosition - Get absolute position
SetPtzAbsolutePosition - Set absolute position
Thank you for clarifying.
Is continuous or relative motion available via any API?
The MIP SDK -
Underneath the SDK uses the RecorderCommandService (SOAP) -