[Healeys] Wheel or Tire Shake

[GUY DAY]

The tyre and wheel may be balanced but the hub and brake parts rotate as 
well.  There are very few fully dynamic machines left that can test when the 
wheel is on an axle as the vibration from the hub etc is normally fairly 
neutral.
Check wheel bearings and suspension bushes.
Have a good look and feel for bulges in the sidewalls and check the tread to 
see if it kinks sideways.
Have someone drive alongside to look at the suspect wheel and tyre to see if 
it is behaving abnormally.
Could it be a driveshaft joint problem you are putting down to wheel shake?

Best of luck,

Guy R Day