Is it a variable, a trigger, or something else?

Here's how to do what you want.

To track each character/module, create a T/F variable with a default value of False. For example, call the variables mod1, mod2, and mod3. 

On the last slide of each module, do this:

• Set the Initial state to Hidden for other character buttons, as well as the button that jumps to the final scenario.
• Add a trigger that adjusts the associated variable to True when the timeline starts. For example, the last slide of the first module would adjust the mod1 variable to True. 
• For each character button that might need to be shown, add a trigger that changes the object to Normal when the timeline starts with the condition that the associated variable = False. These triggers will show the character button(s) only for modules that haven't been completed.
• Also add a trigger that changes the final-scenario button to Normal when the timeline starts with the conditions that each of the variables = True. This will only reveal the button if the user has viewed all of the modules. 

It’s worth the effort to learn about variables and trigger conditions, because they provide the real power in Storyline. Here’s more information: 

• This post provides an overview of variables. It also links to numerous resources.  The Value of Variables | Articulate - Community 
• The User Guide articles about triggers include some about conditions.  Storyline 360: Working with Triggers | Articulate - Community