Thanks for the details. If you already have your tags defined in the system, you can use the Tags API (/api/tags) to get a mapping between tag name and tag ID.

When you know the tag ID you want to modify on a miner, you can do like this with the API for "Managed Miners". It works in a similar way for External Miners as well.

1) Get the properties for a specific Managed Miner:
  GET http://mypc:17790/api/managedminers/{id}
2) Modify the tagList property of the response body
3) Save the new properties for the Managed Miner, where you put the updated JSON data in request body:
  POST http://mypc:17790/api/managedminers/{id}