You're going about it wrong. Or - I should say - not in accordance with Helix principles.
First and foremost, your idea of a common base template to be used on all websites is not recommended practice.
What Helix Documentation States
The architecture does not have the concept of a single common base
template across all templates – which is a practice that is commonly
discouraged as it will often lead to bloated items with unnecessary
fields.
Source: http://helix.sitecore.net/principles/templates/inheritance.html#inheritance
What you should be doing instead, is something like the following:
- Set up your "Favicon" as a Feature or Foundation. You have it as a Foundation module, which will be fine.
- That will, in turn, give you a "Favicon" template. In Helix terminology, this is an
Interface Template.
Defines an interface for solution logic to work against, for example
by defining the fields that are used by a module’s logic or by simply
being a template in the template inheritance hierarchy of an item. Can
also be referred to as a base template.
Source: http://helix.sitecore.net/principles/templates/template-types.html#template-types
Now, for your individual websites - these are Projects in Helix terms. Projects hold Page Templates (and only Projects do this). So you can define a Home Page Template for each of your sites, have it inherit from your Favicon Foundation Interface Template and define a separate source on the Page Template.
Helix documentation describes this as:
To add editor managed settings to the site, modules should define
templates which can be added as base templates to the site root item
for the project layer module, or add settings items inside the site
hierarchy.
Source: http://helix.sitecore.net/principles/multi-site/sites.html#sites
Summary
Make your Favicon Foundation module. Use the Interface Template you defined, and inherit from it on your individual Project Home Page templates. Alternatively, create a settings folder for each site, and place an item (Favicon Settings, for example) for each of the sites in the settings folder.
Since you need to override the field on the template level (not just a default value), the option with the settings folder is best suited for your particular scenario.
