You will not get the new field in the rendering parameter section, the value you are adding will only visible on rendering itself. See the caching section on the rending item under the layout node.
If you will see the
Standard Rendering Parameters-
/sitecore/templates/System/Layout/Rendering Parameters/Standard Rendering Parameters, Caching is a custom type field in it which mean it is not managed by the template you are updating. This custom type field is only updating the rendering field of the item as below -
s:cac="1" s:vbd="1" s:vbl="1" s:vbp="1" s:vbqs="1"
The Caching field is using -
Sitecore.Shell.Applications.Layouts.DeviceEditor.CachingField class from
If you want to manage the caching on Item level then you need to create your custom caching field.