I bought my 1980 TCI earlier this year and its always had a hesitation at speed, around 3K rpm. This string and others on the forum have been great in helping me troubleshoot the issue. As I was doing the tests detailed here by bpeckm, I noticed that my pickup coils described in response #6 were heavily corroded. I used some fine grit sandpaper to gently clean them up...appears to have worked! Went for a cruise yesterday and the hesitation was gone
Still need to do some more test drives to make sure but fingers crossed!
Just one more thing for folks to check, perhaps especially in humid/wet locations or when dealing with a bike from a neglectful PO.