Well, the problem can lie in two places if you are experiencing a buzz in just that one spot. Since the guitar is old my guess would be that the frets need to be leveled/dressed. It could be the frets are just uneven in that area. A buzz in the low E string is always an early indication of uneven fret wear because it's the string with the largest elliptical pattern. My diagnosis is one of two things like I said... 1) The 11/12 fret wire is loose. Even though you can't physically move it around in the fret slot, it could be loose enough that it causes a buzz when you fret there. This can be fixed by replacing that single fret wire. 2) the 12/13 fret wire is high OR the 11/12 fret wire is low. This can be caused by common fret wear. This happens to instruments as the get played a lot. This can be fixed by leveling the frets. You can check this by taking a 3" ruler and place the edge of the ruler on the fretboard so it runs length wise along the fret board... put the ruler so the second fret is in the middle of the ruler. If you can rock the ruler back and forth it means you have uneven frets. Go down the whole fretboard like this and check each fret. Don't just do it by the low E string. Check the fret leveling by each string. If you don't have uneven frets... my guess is that it's a loose fret. GOOD LUCK BRO!