Hi,
Yes, you need to create a custom field of the kind "product". For the type, it depends what you want to do.
If you want just one area where you can write text so that it is added to the specification tab, you can indeed use the type WYSIWYG.
There is no need to "publish it to the "specifications" tab". It will automatically display in there as long as you have text in the field for the current product.
When you edit a product in the backend, you have many different sections including one called "custom fields". The custom fields of the table "product" that you created will appear there so that you can fill them.