It looks to me like the 2 red wires are going through yur motor overload contacts. These wires need to be hooked up in series with the coil wires, so if the overload trips out it will not let the coil on the starter kick in. so from t2 there needs to be a wire to the pressure switch, from the other side of the pressure switch it hooks to the red wire that is loose on one end. Now from t3 there needs to be a wire the same size as the two existing red ones to the other side of the coil wire, I believe this terminal to be on the top right corner of the starter but NOT visible in the picture. Terminals 13 and 14? are just an auxiliary set of contacts and not used in this application. Now the feed goes to terminals L1 and L2 as was stated earlier. The motor leads connect to T2 and T3. When you press in the button on the cover of the starter box it will press the contacts together completing the circuit from L1 to T1 and L2 to T2. Also energizing the wires fromT2 to the motor overload contacts, through the contacts through the pressure switch(assuming it is calling for the need for power), and to the latching coil in the Starter. It will also complete the circuit from T2 to the other side fo the coil. This is assuming that there is a pushbutton on the case to depress the starter initially. If there is no push button, then the red wire that is not connected on one end should hook to one side of the pressure switch. The other side of the pressure switch will hook to L3. Now there will need to be a wire from L2 to the other terminal on the coil, which I believe to be on the upper right hand corner, but not in the picture. With this setup you will need a disconnect in sight of and within 50 foot of the compressor for sure.
If you could take some pictures of the sides of the starter it would help. Clear as mud now? Greg