Let $F \to E \to B$ be a principal fibration, ie obtainable as a pullback from a path loop fibration $PX \to X$. Any path $\gamma: b_0 \to b_1$ in $B$ lifts to a homotopy equivalence $\overline{\gamma}:F(b_0) \simeq F(b_1)$ (by fibre transport). In particular, a loop in $B$ gives a self homotopy equivalence of $F$.
In these Notes is also stated that if $F$ is simply connected ($\pi_1(F)=0$), this gives a well-defined action of $\pi_1(B)$ on $\pi_n(F)$ for all $n$.
Why well definedness of this action depends on simply connectedness of $F$? Isn't this action simply given by $[\gamma] \cdot [f] = [\overline{\gamma} \cdot f]$ where $f: S^n \to F$ represents $[f] \in \pi_n(F)$ and $\overline{\gamma}: F \to F$ a lift of loop $\gamma: S^1 \to B$. Where this action would be not well defined if $F$ would be not simply connected?