If you have a 2017 GS450L, then somebody hacked your engine computer via the built-in Bluetooth, and you need a $500 firmware update at the dealer before it will start again.
If you have a 1905 GS450L, your trembler coil is probably shot. You'll have to take it off the bike and ride your horse down to the dealer for a new one.
However, if you have a GS450L from the early 1980s, it might only have one fuse. (Later models have several fuses in a box, but earlier models don't have that box.) There should be two wires coming off of the battery positive terminal. The fatter one should go straight to the starter relay. (I can see that one in your picture.) The skinnier one should go to the fuse. It will be an inline fuse in a holder, which normally looks like a plastic cylinder about 0.5" diameter and about 2" long in the middle of the wire. The plastic is usually pure white or milky white, but it could be black or some other color. You can open this plastic cylinder to reveal a glass fuse, 0.25" diameter by 1.25" long. If that fuse is blown, nothing on the bike will work. The inline fuse holder should be relatively close to the battery, in the same general area shown in your pictures - within a few inches of the battery, somewhere.
Note that a previous owner may have taped over the fuse holder when repairing the harness - the fuse holder might still be there, but buried under a layer of electrical tape. They may have also cut the fuse holder out of the circuit completely and just spliced the two wire ends that *used* to go to the fuse holder together. In that case, either that splice is bad, or you have some other problem. There is a very small, but nonzero, chance that they replaced it with a blade fuse holder - in that case, you either have about a 1" square by 0.25" thick rubber lump in the middle of a wire, or you should be able to *see* the plastic end of a fuse (probably red or blue plastic) sticking out of the holder. If you have the rubber lump, part of the rubber pulls away so you can see and replace the fuse.
The fact that you get some action when you jump the two big stud terminals at the starter relay with a piece of wire means that your battery isn't totally shot and that the wire from the - terminal of the battery to the engine case is at least somewhat working. If you did that same action on a bike where everything was working perfectly, you'd end up running the starter motor, but the engine wouldn't start (because there would be no power to the ignition coils). If you contemplate jumping those two terminals again, make real sure that the bike is in neutral, or the rear wheel is off the ground, first. If you don't do that, the bike will go for a journey without you. (Jumping those terminals bypasses all the normal safety switches on a bike, like the neutral switch, side stand switch, etc.)
Also, go here
http://members.dslextreme.com/users/bikecliff/ and see if you can find a wiring diagram, owner's manual, or service manual that matches your bike. It's best to get one as close to the year of your bike as you can... the different years are similar but *not* all the same.
I hope this helps!
Eule