88 SPX 2.6

Hey fellas i just got a 88 mm spx with the 2.6 its got a header,2.5 exhust,and a weber carb on it its nice but it won't charge the battery it acts like its chargin but when you turn it off for a few mins its dead again ive put a new battery in it idk what it could be its got a dash clock in it a friend told me that could be it but it goes off when i turn the swich off. i need all the help i can get so plz let me know

Alternator?

idk im gonna get one friday i hope that will fix it if not ull here from me