How to choose the correct TVS diode and how to size it?
A TVS has six key parameters

Ppp Peak Pulse Power. This is the power rating of the devices and should not be exceeded. Take care of temperature derating and design margin de-rating

Ipp Peak pulse current. 

Vwm Working voltage. This is the voltage at which a TVS is guaranteed to to conduct more than the leakage

Vbr(min) This is the minimum voltage the TVS will start to avalaunch the test current 

Vbr(max) This is the maximum voltage the TVS will start to avalaunch the test current

Vclamp(max) This is the maximum clamping voltage at the rated current. 

Working voltage

Knowing the maximum voltage the LRU could be subjected to influences the Vwm of the device (or devices in series) needed. 

In your case, 12V is your working voltage. 

Source impedance

Knowing the voltage and the current of a waveform is required to understand the source impedance of the thread. What's the peak threat voltage, whats the peak threat current -> source impedance of the thread. 

Knowing the threat voltage, the minimum breakdown voltage and the source impedance, the peak threat current can be calculated

\$Ipk =  \frac{ V_{oc} - \Sigma V_{br(min)}}{R_{source} + R_{circuit}}\$ 

This is a pessimistic maximum 

Clamping voltage

With a pessimistic maximum current known, a representative clamping voltage can be calculate via linear interpolation between \$V_{br(min)}\$ at test current and \$V_{clamp}\$ at max current. 
Likewise you have a need to clamp at 13V.

TVS Power

With the conduction current and the blocking voltage known, the Peak pulse power can be calculated.  This needs to be compared against the  energy and the peak pulse power of the waveform.  

How to determine the energy and the peak power of a double-exponential, or multi-stroke. There are a number of ways. One proven way is via the Wunsch-Bell relation where a "K-factor" which is dependent on the type of waveform, is used to approximate teh energy

https://www.microsemi.com/document-portal/doc_download/14639-micronote-120-selecting-tvs-with-ppp-and-waveform-considerations

The problem you will face is finding a device which has a working to clamping that tight.  Take the SMDJ12A-HR. This has a 12V working voltage but 13.3V, 14.7, 19.9V (Vbrmin, Vbrmax, Vclamp). 

My advice would be to clamp at a higher potential but have down-stream R-L-C to "shape" the threat to limit the voltage seen at the load.