Since you are focusing on a specific solenoid then yes they are extremely easy to test.
Follow the advice of using a voltmeter while having someone turn the key.
Solenoids are just dumb switches that let a little power control a big power. The voltage on the little connection or connections is being controlled by the ignition switch. Some solenoids have just one little connection and use the housing of the solenoid for ground via the mounting hardware.
Since your relay is "clunking", a highly technical term used by we that have diagnosed thousands of relay/solenoids then you simply need to measure the voltage on the large terminals while someone turns the key.
Before turning the key get the voltmeter set up and touching one of the large terminals. IF you can follow the large wire to the battery measure that wire/post at the solenoid before turning the key.
Write the voltage down and don't try to remember it. Trust me on this.
Now have someone turn the key. Measure again and if the voltage holds steady close to the previous measurement then move the meter to the other post while the ignition key is still turned.
The voltage on the other side should be the same. A solenoid just puts a jumper together inside the solenoid.
Solenoids become pitted and can easily fail.
Do Not go pulling and tugging on wires until you get those measurements written down. If you accidently fix a bad connection you will not be sure what it was that fixed the problem.
If the voltage on both posts is staying around the same voltage with the key being turned then you need to move further down the line which can be tricky and dangerous.
Follow the big wire to the starter. It may have another solenoid attached and the same measurement technique applies. However being that close to moving things can be dangerous so the use of alligator clips with wires can take you out of range of things.
Once you get the appropriate measurements then you can easily diagnose the problem with confidence.
Just jumping in and cleaning battery posts and grounds can solve the problem but one would not know for sure if there is an intermittent solenoid.
H/R Endeavor 2008
Ford F150 toad >Full Timers
Certified Senior Electronic Technician, Telecommunications Engineer, Telecommunications repair Service Center Owner, Original owner HR 2008