Hi.
This is David.
My uncle had the same problem with the second string. The reason was the pickup (it is in the bridge of the guitar). As you said your guitar is quite old. The pickup has probably bent during this years. You should better show it to the men who understand something in this business, as my uncle did. And don't try to do it yourself.
Now my uncle's guitar works perfectly though he didn't change the pickup.
Good luck.
By the way, I try to find such a guitar, But the cheap one (may be second hand). Please give me some information if you have.