Hi there, Robert!
Sounds to me as if you do indeed need to adjust the play in the headset bearings.
I usually lock the front brake and then try to push the bike back and forth, feeling for (rather than listening for) a "clunk". NOTE: The "clunk" can sometimes be play in the brake pivots, so another way is to put the bike in a repair stand with the wheels clear of the ground and try to move the forks directly back and forth, feeling for the same sort of clunk.
To tighten it, be sure to loosen the stem's steerer-clamp bolts *and* any other clamped accessories (such as a Thorn Accessory T-bar).
Tighten the top-cap adjusting bolt *just enough* to remove the play, but stop before adding any drag. Basically, it is a tighten-check-tighten-check sort of thing and requires very little actual tightening. You don't want to reef down on the adjusting bolt else you'll squash the lot.
Realign everything and tighten the clamp bolts again. Done.
It is common for steering play to develop, and not just as a result of bearing wear. With use and road vibration, most headsets seem to seat a bit further -- the crown race hammers down a little onto the crown seat, the cups go a tiny further into the top and bottom of the head tube, making the lot have a bit more clearance than when new.
Best,
Dan.
