Opposite sigma and pi hopping signs in a p-orbital chain

For a chain along $x$, translated $p_z$ orbitals form a side-on bonding combination at $k=0$, whereas translated $p_x$ orbitals form an end-on bonding combination at $k=\pi /a$. With $E=ϵ+2t\cos ka$ and identically translated orbitals, these correspond to $t_{\pi }<0$ and $t_{\sigma }>0$. Changing the sign convention of the hopping Hamiltonian changes the parameter signs, not the physical band extrema.