I understand how confusing this can be. Start circuits can be complicated.
I just looked quickly through the above posts and suggest that you also double check the "ground" (DC negative) cable and connection to your motor. If you have already done it all good but it is often a cause of intermittent starter problems (and alternator
problems). If that cable and connection are not sound then a weak current
will be available to the starter. I can't tell you where this cable is connected to the motor. Sometime it is to the base flange of the starter. But it will be a big cable and should be at least the same size of the starter positive cable (the big one to the solenoid). Take it off, clean it, and reconnect it - tight. Like you did the others. I have found them loose before and I should have suggested it previously. My favorite adage is "check the ground first" and I didn't say it here.
The first pic of the C channel bracket shows a little "baby" solenoid. It is normally not part of a starter circuit but I have seen them in circuits before. It might also be part of the glow plug
circuit if you have glow plugs. It can NOT carry enough current
to run the starter but it can allow a small current to provide stronger current to the solenoid on/off that is on the starter itself. That can help with voltage drop issues from the key switch to the solenoid. You'll have to trace the wires to figure out what it is for. But it will have 4 (or 5) contacts on the bottom side. The wire going to the one labeled "30" is the main power lead that is switched on or off by the little solenoid (same as for the bigger starter solenoid). The output of the solenoid is on contact "85".
So it goes to the item that is being turned on or off by the little solenoid. Contacts "86 and "87" are the control wires. One will be a ground and the other will be control wire. E.g. if it controls the glow plugs (which need a strong current) then the "85" will go to the glow plugs. "30" will go to a battery positive source (like to the starter positive).
One of the other wires will go to the ignition panel for the glow plugs. I am only giving this as an example because it may not be what you have.
But beware that some little solenoids like this can be NO - normally open, or, NC - normally closed. They can also be used to stop motors that have an electric
stop solenoid - a lever that shuts off the fuel
to the motor. I doubt your little motor has one, but if you do, then that part has to work as well for the motor to run but it wouldn't prevent the motor from turning over if it didn't work.
Re: voltage drop - I would do every thing else before trying to measure this. It is confusing. And it can only be measured when current is flowing through a wire. There will always be some voltage drop through any wire.
But you made a comment which I may have misunderstood. It sounded like you did not get 12 (or 13) volts measured from the big positive cable to a good ground. A "good" ground is what you need. So I would go to the battery negative if your lead will reach and the other lead to the big positive on the solenoid. The start battery switch should be ON. You should get full battery voltage on that connection. If you don't then the circuit is bad either from the battery to the battery switch or to from the battery switch to the starter solenoid. Then check the voltage from the positive on the solenoid to the motor (some bare and clean metal) but not to the big negative cable I mentioned above. If you have good voltage (same as measured at the battery then your main battery power to the solenoid/starter is "probably" good.
BUT - you can see full voltage even with a bad connection or wire as voltage can be measured off a weak connection or a small wire. And a weak connection will not allow enough current to flow to start. (A voltage drop test can show this but you can only see it when you try to start the motor and the solenoid clicks but the starter doesn't turn over. You can only measure it while you have the start button or key switch set to start. When you release the switch, as you would when you get the motor started, you no longer have big current flowing to the starter and you won't see a voltage drop. You will always see some voltage drop as it is caused routinely in a start circuit. But it can be large if a connection is bad.
You would measure it from the battery ground (on the battery) to the big positive post on the solenoid. A buddy helps do this unless you have a remote
starter switch or have long enough arms to reach the starter switch and watch the meter at the same time. I always carry a couple of extra leads with my meter with alligator clips on both ends to extend the reach of my meter leads.
You said the solenoid and starter checked out so it is in the ignition/starter circuit or in the big battery cables
(positive and ground).
I hope this may shed some additional light on the matter. But I'd double check the battery ground/negative to the engine
first. After that it is a question of finding good voltage at each part of the ignition circuit - power to the ignition panel, power out of the starter switch, power to the starter solenoid "on" wire (what makes the solenoid click). I draw pictures/diagrams myself as it disciplines me to draw a complete circuit and shows sometimes a part I missed. And you will certainly understand that part of your boat really well after that. And put the diagram in your boat docs. You may need it again. Good luck. You'll get it done.