Thermopower of molecular junctions is sensitive to details in the junction and may increase, decrease, or saturate with increasing chain length, depending on the system. Using McConnell's theory for exponentially suppressed transport together with a simple and easily interpretable tight binding model, we show how these different behaviors depend on the molecular backbone and its binding to the contacts. We distinguish between resonances from binding groups or undercoordinated electrode atoms, and those from the periodic backbone. It is demonstrated that while the former gives a length-independent contribution to the thermopower, possibly changing its sign, the latter determines its length dependence. This means that the question of which orbitals from the periodic chain that dominate the transport should not be inferred from the sign of the thermopower but from its length dependence. We find that the same molecular backbone can, in principle, show four qualitatively different thermopower trends depending on the binding group: It can be positive or negative for short chains, and it can either increase or decrease with length.