Sad story

RE: 2003 Tohatsu 18 MFS18B2
I crossed the battery leads while connecting the battery, that is +to - and- to +. I did not realize that until the next day when I corrected my mistake. After correction and replacing the fuse the electric start worked a few days and then stopped working. The motor starts by hand and runs fine but I want to restore the electric starter. I suspect the solenoid and want to remove it and test it independently of the other switches, shift etc. I can not figure how to get it out of the rubber shield it resides in.

When I push the start button and nothing happens not a sound or a click. When I cross the solenoid leads with a screw drive the starter works fine, and the motor starts.

1) Could it be the solenoid or what else could it be?

2) Any way of testing the solenoid without removing it; note I do fear all the spaghetti wiring to the different controls and switches.

OK, you have verified that the starter motor is good. Now to test the rest of the components that operate it: If you jumper 12v to the trigger lead of the solenoid (there are 2 small wires on the solenoid -- one is grounded to the block, and the other gets the 12v signal to trigger), it should click and engage the starter. If not, it's bad. The solenoid is just a "switch" so that you can feed low-current through the controls (such as the start button, neutral safety, or RC key switch), and then... when the solenoid receives that signal, it "jumpers" the high current wires to the starter. Possible problems are the solenoid itself, the start button, or the neutral safety switch (or associated wiring). You can do a lot of tests with a good analog volt/ohm meter. The start button should show about 0 ohms when you press it. The neutral safety should also show about 0 ohms in neutral. The low current then travels through both switches to the solenoid. Full testing info is in the Factory service manual. Be advised that you may have also blown the rectifier when you reversed the battery... the fuse may have saved you, if you are lucky.