Welcome to the forum!
Which tutorial are you following? Some of those features you're using have been changed in some relatively recent versions of Inkscape. And if the tutorial you're following is older than those versions, you might be seeing a conflict related to that.
You probably don't need to use Pattern Along Path, to be honest. You could use it, for sure. But if you're using the Triangle In option, then the Pen tool is automatically applying a different path effect, called Powerstroke, which you can see in the the Path Effect dialog in your screenshot. And it probably will do what you need, for flourishes.
I'm not sure why you want to adjust the width. I mean, I understand why you would want to, it's just there could be different reasons, and I don't know what your specific intent is. So if you could explain that, and if I don't already give you a way to do it, with my next comments, we can tell you how.
For now, I want to tell you about the powerstroke LPE, and that might give you everything you need. First, click on the Pattern Along Path item in the Path Effects dialog, and then click the minus sign. That will remove that path effect from the object.
Next, switch to the Node tool (if not already using it), and look closely at the path. Do you notice at least 1 or 2 nodes which are pinkish rather than gray? Grab one and drag it. Ta-daaaa!
If you need some more pink nodes, place the Node tool pointer over an existing pink node. Hold the Ctrl key while you click once. Yes, it looks like nothing happened. But grab that pink node and drag it away, and you'll see that the original node is underneath. So it did make a new pink node, and you can just drag it along the path to place it where you need it.
If you ever need to remove a pink node, put the mouse over it, then Ctrl + Alt + click once.
If you really want to use Pattern Along Path, then I would remove the Powerstroke LPE. Here are the instructions for PAP:
http://tavmjong.free.fr/INKSCAPE/MANUAL/html/Paths-LivePathEffects-PatternAlongPath.htmlLet us know how it goes