testarossa bad running on cold start

Does the transistion from bad running to good running always occur at the same indicated temperature on the water temperature gauge, or is it more random?

Because the voltage coming from the alternator would be different values under different conditions, there are voltage regulators inside the injection ECUs that produce a steady 8V to run the injection system. Since 12.3V is still much above 8V, I wouldn't think that should cause the injection system grief, but having this bimodal condition of 12.3V DC or 14.5V DC doesn't seem like a good sign for the alternator. You might also try measuring the AC voltage between the battery terminals when it is showing 12.3V DC or 14.5 V DC -- a high AC value (anything over like ~0.5 VAC) would be another bad sign for the alternator.

Not great, but, if you are getting a quick initial first light-off during cold cranking, it must be enough to open the cold start injectors. The +12V signal does pass thru many relays and connections, so if you'd like to try tracing it backwards to see if it's a little higher somewhere upstream, the path is:

cold start injectors - t87 on relay E (...113 in the black box) - t30 on relay E - t30 on relay D (...101 in the black box) - t87a on relay D - the CN (orange/black) wire on the water thermoswitch - the R (red) wire on the water thermoswitch (where you are already getting +12.3V or 14.5V).

 

Definitely not normal -- and indicates that you have an ignition problem. Verify if you do, or do not, have spark on both banks during the initial starting attempts. If the 7-12 bank is not working, this will definitely give the symptom of "cranks, fires, runs for 10 seconds, stalls" (because the tachometric relay will turn off the fuel pump relays if it isn't receiving the proper signal from the 7-12 coil+power module when you release the key to Pos II).