It is definitely the alternator. Tomorrow I will see if they pay me and take it to an electric and I tell you.
Only out of curiosity and to continue the issue that can serve another person, regarding trying if the car has any short.
As many know (and the occasional I reaffirm here) the easiest way to test if an electrical system has leaks is to remove the battery connectors and connect them dark to see if they throw sparks. As some say, if sparks come out the electrical system has a leak. But regarding this there are several doubts, to see if we generate a debate regarding it.
This famous test is done with the key withdrawn and of course with the 100% off vehicle, otherwise it does not work. But there are several "buts."
First, if we think a vehicle is always going to have consumption, whether the memory and time of the radio and/or the digital clock or analogue. If these did not consume energy while the vehicle is off every time we turn on the vehicle we would have to be configuring the time and radio. Moreover, mentioning modern cars that have computer modules, they are consuming current. Then: every vehicle has normal consumption and therefore when we place the connectors to the battery they will sizzle. Now others say: "Before doing the test disconnects everything that generates consumption." If one knew what electricity is consuming, it would not do the famous test, and finally it is not the grace to disconnect accessories to see if there is consumption or not.
Then my question goes: how "homemade" can you know if a car has consumption?