This strikes me as an odd way to put it, as in the course of checking those components one would normally be checking whether or not the wiring was okay. In other words, if proper testing was done, there should be no question as to whether or not there’s a wiring problem.
I assume the problem is that the starter will not crank. (If that is not the problem, provide us with the symptom(s) observed and we’ll go from there.)
In my experience (automotive), most solenoids have one small pole (the “trigger”) and the winding is grounded through the solenoid housing to the body/frame (remotely mounted solenoid) or through the starter housing (starter mounted solenoid). If there’s a second small pole, it provides power to an additonal circuit during cranking. Maybe it’s different on lawn tractors.
Basic testing can be done with a test light. A good place to start is at the solenoid.
>The battery cable pole at the solenoid should show power all the time, and its connections at both the battery and the solenoid should be clean and tight. If not, repair or replace the battery cable.
Now go to the trigger terminal on the solenoid.
>It should show power when the ignition/starter switch is turned to the “start” position. If it does, that indicates the components and wiring up to that point are okay. If it doesn’t, continue testing at the ignition/starter switch.
>If it’s a remotely mounted solenoid and has power, but doesn’t click and connect the battery cable pole to the starter cable pole, the solenoid is faulty. (If it has a separate small ground pole as described by HoneyBadgerDC, ground that directly with a jumper wire and retest – no click = bad solenoid, clicks = bad ground wire which should be repaired or replaced.) ETA: If it’s grounded through the housing, make sure the mounting makes a clean tight connection to the body/frame.
>If it’s a starter mounted solenoid and has power, bypass the solenoid by using a good-sized screwdriver to directly connect the two large solenoid poles together. Starter cranks now = solenoid not working, no crank = bad starter. Solenoid not working can be due to faulty solenoid or faulty starter – this is not a problem with automotive starters as the starter and solenoid are only available together as a unit.
If there is no power to the solenoid trigger during “start”, the next thing to check is the ignition/starter switch.
>One terminal at the switch should have power all the time. If it doesn’t, test the wiring between the battery and the switch.
>If it has battery power per above, and it’s a combo ignition/starter switch, one terminal should have power when turned to the “on” position, and another should have power when turned to the “start” position (a starter-only switch won’t have an “ignition/on” function). If not, the switch is faulty. If it has power at “start” but there’s no power to the solenoid trigger, test the wiring between the switch and the solenoid. If it’s a combo switch and has more than three terminals (battery, ignition, start), the function of the additional terminals should be determined before judging the switch.