Bosch WOL 2200. Press start. Clicking heard. then a second clicking then nothing - assumed electrical / solenoid problem

Check drain pump for obstructions

A Defective control panel is about the only thing that will cause this.

Depends on how cold it's getting outside. Cold weather is ******* a battery. Try load testing your batteries. That "clicking" noise makes me believe that it's trying to start, but it's not pulling enough amps. Considering everything that you've already replaced, I would start there. Assuming you've already made certain all of your connections are good. Also, make sure the ground wire for your electrical system is good. Not loose, corroded, etc...
You can even call the local golf course and ask to speak to the golf cart mechanic. I would get several calls a week from drivers when I worked as a diesel mechanic.

check pump for blockages or pump gone

the way you are describing it the engine is seized
but if the engine will turn over on the flywheel bolt
then it could be a couple of things
using your kick start (if your kick start does not move when pressure is applied then your engine is seized)
(remedy) total engine strip
("your kick start just goes up and down not doing anything")
seized clutch
remedy strip your clutch and clean up
("if a clicking noise is heard when using the electric start but your engine does not move it is your starter solenoid")
take off old one and replace and replace

Battery is most likely - they drain fairly quickly when sitting and the electric start will kill one in 15-20 failed starts. Pull it, put it on a charger overnight, put it back in and try it again. Does it start with the kicker (assuming you have one)?

Assuming your battery is properly charged and has a good connection, it's your starter solenoid (relay) that has failed.

The starter solenoid receives a large electric current from the car battery and a small electric current from the ignition switch. When the ignition switch is turned on, a small electric current is sent to the starter solenoid. This causes the starter solenoid to close a pair of heavy contacts, thus relaying a large electric current to the starter motor, which in turn sets the engine in motion.

If a starter solenoid receives insufficient power from the battery, it will fail to start the motor, and may produce a rapid clicking or clacking sound. The lack of power can be caused by a low or dead battery, by corroded or loose connections in the battery cable, or by a damaged positive (red) cable from the battery. Any of these problems will result in some, but not enough, power being sent to the solenoid, which means that the solenoid will simply make a clicking sound, rather than setting the starter motor in motion.

If these items are all okay, it is likely you need to replace the solenoid.

a clicking sound means there was enough electric power to engage the solenoid, but not enough to turn the starter. battery is low

I can think of 2 possibles,it could be a bad battery cable or an intermitent short in the starter solenoid, check or have the battery cables and there connections on both ends first not only are they a cheaper fix but the problem you describe sounds like a current flow issue.Test them with or have them tested with an ohmmeter they should show o ohms resistance,and while not attributed to the problem I do not reccomend using Bosch spark plugs of any variety,the best plugs for any Japanese vehicle are NGK's,this comes from my personal experience with them and other techs that I have worked with.

I have a Bosch wol 220 washer, it is not clearing the water on spin. I have checked for blockages and it appears clears.