2001 Ford Mustang 2001 Ford Mustang battery drainage

Electrical problem
2001 Ford Mustang 6 cyl Front Wheel Drive Automatic 72K miles

I recently bought a used 2001 Yellow Ford Mustang from its owner about 3 months ago. The very first day I drove it, it died out on me! I told the owner and he took it to his Machanic to figure out the problem. He said the reason why it died out was because the alternator was bad and the battery was completely drained! Since the owner offered to fix the alternator, I decided to keep the car. A few weeks after both the alternator and battery was replaced, my mustang wouldn't start. I tried to get in touch with the owner, but I haven't been able to get in touch with him since, so now I'm stuck with a car that doesn't start. If I jump it or charge the battery it will be fine for that day, but if I have it off over night it won't start in the morning. I even changed the terminals and battery connectors because I tought maybe it was too corroded and the power wasn't reaching the battery to keep it charged. But still nothing worked. I took it to the family Machanic and he kept it for over two weeks. When he finally called me he said that he was able to fix some of the draining problem and he also found that if I just continued to start and drive the mustang around everyday, it would start up fine the next day. But he said if I don't drive it for more than two days in a row I would have to take off the terminals and reconnect them every time I wanna drive it. I asked him if there is any way to solve the problem, so I don't have to keep taking the terminals off and having to worry if the car will even start up! He told me that the only way to fix the problem is to obtain a certain part that is located in the dashboard, but he said the part was obsolete and they stopped making that it years ago. And he also said he isn't 100% sure he can fix it because he would have to find the part, get the number on it, and then he would have to call the mainland, cause I live in Hawaii, to see if they even have the certain part and could send it to get it fixed there. So knowing all of this, do you know what part he is talking about? And do you have any other options or advice for me on what to do? And do you think this is really all thats wrong with my mustang? Please help me figure out the best thing to do and what that part is called.