Call to default values (MySQL) in a procedure
The point of "default" values is that they are the default values.  You Don't need to list them in the insert query at all.  They'll be inserted automatically.

To pass CURRENT_TIMESTAMP as a parameter, you probably need to use the equivalent pseudo-function, CURRENT_TIMESTAMP()... which is the same as NOW()

Stop and consider DEFAULT CURRENT_TIMESTAMP ON UPDATE CURRENT_TIMESTAMP.  The default value here is only CURRENT_TIMESTAMP -- ON UPDATE ... is a completely unrelated directive, so here again, you need to just pass NOW() or CURRENT_TIMESTAMP() if you want to pass these into procedures... though that us unnecessary if you modify the inside queries not to specify the columns you are free to exclude, because they have default values.