From the previous posts, it is obvious this has bothered me for quite some time.
Now it is fixed. The problem turned out to be the tach amplifier I purchased from someone on this site (I think). It is the one with the blinkin-lights. He makes them, and they generally work quite well, or so the forum indicates. I remember when I first got it, I tried to contact him about it, and I don't remember if he ever replied. I kinda think not, but am definitely not sure.

My memory is not what it was 50 or so years ago.
Anyway, after I replaced the socket and all wires the tach amp plugs into, again, I got an old amp that worked sometimes. Plugged it in and wiggled it until the tach worked. I tried the turn signal and got in no bounce. Horn did not cause a bounce either. I then replace the amp with the blinkin-light one and everything returned to the bouncy condition. Turn signal caused the tach to jump in time with the signal, and the horn caused it to peg all the way to the right. Went back to the old style amp, used bubble wrap to hold it in place, and the tach needle is steady as it should be (I now have the problem of the intermittent tachometer again, but I think I will keep that instead of the one that bounces with the turn signal. At least until I can get another tach amp from somewhere.)