Not quite the answer, but I will post my findings and the workaround I chose to use;
The T4 code generation template (the file attached to your .edmx file with the extension .tt file) contains code for generating C # using the data available in your model, I suspect the code in line # 204 (may be located on a different number lines in your version) to contain a minor error.
Screenshot of my active project and solution developer: 
This line causes erroneous enumerations:
this.GenerationEnvironment.Remove(this.GenerationEnvironment.Length - 3, 1);
This presumably removes the generated code characters that were added by the enum generator to remove the last , from the listing, as this is not necessary.
I tested the functionality of this by adding output before this line, I tried to create an enumeration that would output MyEnumMemberName = TEST, and find that the output contained MyEnumMemberName = TES,
Using this, I found that changing the string to:
this.GenerationEnvironment.Remove(this.GenerationEnvironment.Length - 2, 1);
solves my problem.
It is currently not possible to check if this works on machines that already generate the correct code, but I hope this helps some of you. Good luck.
Fixation
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