A few suggestions on popular ways to spot scripts which you should move to the head and make them render-blocking to avoid unpleasant visuals:
if you have a carousel upfront, you'd want to move to the head both the carousel script and any libraries it might depend upon (jQuery is popping up often as a dependency).
If you're having a hard time finding out which JS file touches those elements, try searching in the JS files for the element selector OR any attributes that stand out to you while inspecting the element.
Discovery can be done by discarding individual JS files in an attempt to see which one is causing that special element to misbehave, giving you a good starting point.
There is no automated tool for this, as the usage scenarios can wary so widely, it's always a step-by-step try and test process.
You can also use the defer attribute on the script tags.
When you use the defer attribute those script tags no longer block rendering regardless of where they exist (in the head or at the end of the body).
Deferring does mostly the same thing as moving the script tags at the end of the body and is well supported - defer attribute browser support