Hi @Brenden K ,
App Service scale-in logic will observe the rules configured over a 5-minute sliding window duration. If the scale in rule(s) is not triggered within that 5-minute window, the instance will remain. However, if they have been triggered, those instances will begin shutdown.
I don't know if there are other custom metrics you can observe on your Web API that relates to the work being done on your dependent resources but utilize the best practices guide. If you find that none of the rules fit your workflow, you may want to consider applying pipes and filter pattern to your application design. Using Azure Functions may also be a more a suitable option that allows you to use durable functions to maintain stateful data.
EDIT: App Service will follow IIS default timeouts. If a scale-in operation is requested, the instance being spun down will process any "in flight" requests for 90 seconds before being terminated. During this time, any new incoming requests won't be sent to that server.
Regards,
Ryan