You are going to see a lot more fork flex from your 86 than from the 01. The forks on the early model bikes were not nearly as rigid as the later models.
I forkbrace may help you in this situation. I installed one on my 02 and it helps tremendously in grooved roads and dirty air. In my opinion a good set of tires will do more to correct this issue. A few things to check; do you have any cupping, low air pressure in tire, and how is your pre-load set on your forks?