Hi,
external_form is standard in concrete5 (not to be confused with the Extended Form)
I can integrate with external_form own forms.
In the folder concrete/block work/external_form/forms/ is a file "test_form.php". Its a model of a form and it works.

But not their own forms:

Fatal error: Call to a member function runTask () on a non-object in
....com/concrete/blocks/external_form/controller.php

Since I assumed that in my form was a mistake, I've duplicated the test_form.php and added one word and saved as test.php.
But even when including these nearly Originally sample form I get the error.

I use concrete 5.4.1.1, in the older installation 5.3 the forms works.