What can happen with bearings is that if they receive a shock, it can force the balls to dent the bearing race. This is called "Brinelling" (there is a Brinell method for hardness testing based upon making dents in metal). Too, if a bike sits in one position for a long time you can get corrosion that forms detents in the bearing races. Last, you can bend axles (or less frequently headsets) so that the cones and cups aren't aligned, which can cause the searching phenomenon you observed.
Take the stem out of the headset. (Helpful hint: do this with the headset over an old towel with the bike lying down if you suspect that you have cups and cones with unretained bearings. Or if you don't know that you don't. This will limit bearings flying all over the place. Remove the fork and clean the cups, balls and cones (mineral spirits in a big plastic peanut jar, and an old toothbrush is what I use.
Inspect the bearing cupes and cones (the lower cup and upper cone will still be in the bike frame). You should be able to see if there's dents or rough spots. Worst case, you need a new headset. Or, you need to go on ebay and find a matching cup and cone. If the bearings look good check the fork steer tube with a straightedge to check for bends. Let us know what you find.
BTW, if the effect is very small and you don't notice it while riding, you could just clean the thing up and regrease the thing and reassemble. Easy to obsess about things that don't really matter.
Last edited by WizardOfBoz; 08-19-19 at 06:10 AM.