Either the home button extension cable is partially damaged or teared (really hard to tell but it's easy to damage) or the home button cable itself on the home button is damaged.
Best bet is to try another home button extension cable first (I buy with the metal shield to avoid the hassle of trying to install the home button cable without it pre-assembled).
Here is the part I am talking about, ignore where it says replacing the cable stops touchID from working, it is false and only applies to replacing the actual home button itself.
[product|IF268-026]