Do you have spark? Are the plugs wet after attempting to start it?
The thing with the prongs (part of the brake light switch maybe?) may not be causing this problem but it will surely cause other problems in the future.
And for heaven's sake move that regulator/rectifier before it melts the wiring harness. Those fins on it are not just to make it look good but because it can get hot (fins = more surface area to dissipate heat). It needs to be located where there is good airflow past the fins and bolted down securely.
BTW, I seem to have missed this when you joined so welcome to the forum. Please add your location and your bike's model and model year to your profile so that you don't have to remember to tell us every time and we don't have to keep asking when you forget (see Forum Settings link in my signature).
And welcome to the world of antique vehicle ownership (they own us, not the other way around). Your bike is about 4 decades old and in spite of the changes that have been made to it may or may not have had all of the maintenance necessary to keep it safe & reliable so it is highly recommended to download the Factory Shop Manual for your model (available through the CX Wiki - link in my signature) and go through all of the service procedures, regardless of whether your bike has reached the specified mileage.
I also recommend looking on all rubber parts with suspicion because rubber does not age gracefully. Your tires look pretty new but it wouldn't hurt to check the date codes on your tires and replace them if they are over 5 years old no matter how good they look & feel (old rubber simply cannot flow around the irregularities in the asphalt well enough to grip, especially if it is cool or wet).
It always amazes me when someone makes all sorts of changes to a bike without addressing something as basic as replacing the original rubber brake line. They really should be replaced every 2 or 3 fluid changes (= 5 or 6 years) so I recommend shopping for modern stainless braided ones (they last practically forever and double the life of the fluid).
Of course, that won't matter if the line isn't connected to the master cylinder....
And don't forget things like the rad hoses and the boot between the engine and swingarm (they can crack on the bottom where you don't see it).