@Matthew Dailey Welcome to Microsoft Q & A Community Forum. Yes, its recommended to use Managed Identity for authenticating Azure resources from the runbooks. However, the existing Start Stop Solution uses "RunAsAccount" for authentication. I would suggest you create RunAsAccount for this scenario. For information on how to create RunAsAccount , you can refer this document.
I assume you have installed Start Stop Solution v1 version. I would like you to know about the next version, which is in preview right now. This new version (v2) offers all the same functionality as this one but is designed to take advantage of newer technology in Azure. It adds some of the commonly requested features from customers, such as multi-subscription support from a single Start/Stop instance.
Start/Stop VMs during off-hours (v1) will be deprecated soon and the date will be announced once V2 moves to general availability (GA).
Also, we will update our documentation with the information that you have requested.