EOS stands for End of Stroke switch. Its the switch your flipper activates. To test the switches go into switch edges test and activate them to see if they are working.

EOS is edge of switch, found on the flippers the only switch underneath the playfield connected to the flipper assembly.

Your manual will have a list of all switch location find that page. Then find the location on the playfield of the ones that came up on the report. Once you find them you need to trouble shoot them if its a regular switch and it clicks fine no sticking you may have to just bend it a bit so it sticks up more on the field (not too much or it will cause ball to catch). If switch is sticky and doesn't have the crisp click sound you will have to replace the switch by de-soldering old one out and soldering a new one in.

The GI lights out you need to track down the source on the string first check your GI fuses (manual will show you where they are and type) to make sure none look bad or are blown. If one is bad you need to change it out that would be the best first step to take. It could also be loose or cut wire, or bad solder joint, or a bad socket in the string, or loose connection from string to the board it requires a lot of trouble shooting.

You could use needle nose pliers, if it is too far apart bend them a bit closer from the bottom of leaf NOT the tip, if too close bend it out a bit from bottom as mentioned above.

Yes. Or you can do it manually under the playfield.

Also, you have a page in the manual that shows a grid of rows and columns. Check to see if all of the switches are in the same row or column, if they are, then you know it isn't the switches themselves, but the chips that control them.

Here is the best advice I can give. LOOK! 80% of the time a problem can be seen with the eyes. Just like the problem I had with AFM. When I finally LOOKED at the roms I could see one wasn't seated all the way. Use your eyes.
With the GI lights...Check the connectors on the largest board for burnt ones. Common problem.
With the switches, put it in the switch edges test and try each one with your finger. if it don't work try taking it off and readjusting it from underneath..

with the flippers, make sure the non working flipper looks just like the working one. start there.

Look. get dirty. If ya get stuck ask here. then look again.

Oh and the right popper has opto switches. You will have to test those with the playfield up and in switch test. then use a piece of paper or your finger and put it between the optos to test them.
there are two sets of optos for that popper. I believe it's the Hole in One popper.

That fuse blowing when you cradle the ball sounds like high power isn't being disengaged to the coil. Is the end of stroke switch being hit? When you cradle the ball it should switch over to low power to power the coil to prevent the behavior you're seeing...

Yes, if your coil is burning, you will smell it. Sounds to me the EOS switch is not closing all the way. It should close right before the flipper gets to the all the way up position. You may have to buy a new coil but get the switch adjusted correctly first or you will burn another coil.

Could also be bad or dirty flipper optos. Clean inside the U shaped optos with a Qtip. These are on the rectangular boards at the buttons.

Could possibly be the transistor is bad.
Flipper seems to work fine, but gets very hot and eventually starts to burn and smell. Often the flipper will get stuck in the "up" position. On Fliptronics/WPC-95 games, the hold TIP102 transistor for that flipper is shorted on, and needs to be replaced.
Q11 is the lower right Hold TIP102. Q9 is the lower left Hold TIP102.

Any modern flipper coil has two windings. Low power to hold the flipper bat up and high power for the initial stroke that propels balls upward.

On pre-fliptronic games, pressing a flipper button would cause the high power to kick in, sending the flipper upwards. The EOS would register and the low power would take over to hold the bat up. In other words, the EOS was very important otherwise flippers would be held up by high power all the time!

With fliptronics, the computer regulates this switch and does not rely on the EOS anymore to switch from high to low power. It will do so automatically after a couple of milliseconds. It does hoever use the EOS switch to detect flipper drops (from fast balls) and to switch from high to low power earlier than the predefined couple of milliseconds.

In other words, a game like NGG does not rely on the EOS switch to change from the high power winding (initial flip) of the coil to the lower power (hold) winding.

How does the EOS work to detect a flipper bat drop? For example, if a ball falls down from a height on the flipper tip: the hold power will not be enough to keep the flipper up. The flipper will be pushed down just a bit from the impact of that ball and by this the EOS makes contact (opens/closes, depends on game generation). The computer senses this EOS state changes and performs another "power boost" for a couple of milliseconds by switching to the high power winding. This happens so quickly that it effectively prevents the flipper bat from going down more than maybe a millimeter. You shouldn't really notice this at all. After the power boost, the flipper is up again, the EOS is closed/opened again and low power takes over.

Now you'll hopefully also understand the importance of the EOS: if set to tight (activate too early in the flipper stroke) then the stroke will no be powerful because low power kicks in too soon. But it will also cause the flipper bat to be slow to react to ball impacts pushing it down. You'll notice in that case that a ball falling fast on an upright flipper will push the flipper down quite a bit. That's not good. In other words, this is where good EOS switch adjustment is very much needed!