Frank Thompson wrote:
doing trouble shooting on 3 yo lightly used keyed brush mower.. which is most likely and which is most unlikely candidate for problems.
ignition switch
solenoid
starter

Battery is fully charged & when key is turned to start only a clicking sound occurs

You missed battery on the list, next cables, battery to starter, battery
to ground. Battery may look good but unless you check it
with hydrometer or load test..... Try jump start.