I’m sorry but I don’t understand how to animate it to give the same effect. Let’s say I create a long horizontal line split horizontally in the middle by two masks (e.g. one set to subtract and the other as its inversion and also subtract). Then I can animate mask expansion to make the line continuously thicken but without the narrower tip. Could you be more specific about the animation part, please?
I need almost the same as the effect ‘Write-on’ with animated brush position and brush size, but the narrow line must expand with time to a certain point like this: 
By the way, can this not be done with expressions? I’d like to just set the path and generate the line programatically.