Ignition Switch Question and Running Light Problems,

So today I got back on the rollercoaster of emotions that is working on the good ol kz. I've been struggling with a running light problem. I can get the brake light to work when I depress either brake switch, but no running light in the tail light. Both filaments are good, there is continuity for the entire stretch between the red wire at ignition and the rear of the bike, ground is good. Ignition switch only has continuity to yellow and brown wires when in on position, but not red or blue wires, but does give  continuity to red only when in park setting. Any ideas as to the problem? Also, if anyone has pictures of the internals of the ignition switch for me to take a look at and compare I would greatly appreciate. Thanks!

Check both sides of these two fuses.
Engine running
Meter on DC V
Black probe on negative battery post
Red probe on positive battery post
note voltage

move red probe to both sides of each fuse
you should have 4 voltage readings
voltage should be close to battery voltage

schematic courtesy of Mcdroid
 

So I have yet to get home and check my voltage and will today. But I was doing some thinking, a rare occurrence, but shouldn't the red wire coming from the ignition switch be hot in the on and park position? If it is then I think my switch is the problem. I will however check my fuse voltage and all that tonight, but figured I'd run the idea by another set of eyes and knowledge. Thanks!

What year and model do you have?  The wiring pic  posted appears to not have running lights in front or back, rather just turn signal lights.  There would need to be another line and connection in sockets to have running lights and there would need to be dual filaments in the bulbs. At least that is how I understand it, am I mistaken in my understanding?

The red wire just goes to the tail light, which makes me believe it's only for the Park position.

It is a 1980, and the wiring does look correct. Im going to check fuse voltage now. The tail light is a running light, it had worked in the past, not recently.
 

I was thinking that, but I took a look at the bottom of the wiring diagram, it shows the switch in the on position connecting power to the red wire, Im going to try to jump the ignition switch and see if its not bad contacts.
 

Update, I think its the ignition switch, I jumped the red wire to the ignition wire while the switch was in the on position and all worked as expected. Now to find out why this dang switch won't work, or figure out how to jump it so that it works just well enough for me to buy a new one. Speaking of, anyone have an extra? 
 

The ignition switch blue wire (which supplies the ignition switch red wire with 12v in the run position) gets it's 12v from the brown wire through the fuse I marked.

Continuity measurements can trick you into thinking a circuit is ok. You have to use voltage drop testing to spot problems in a circuit.
Check your fuse voltages first.

I got called into work last night so I didn't get a chance to check voltage, but I check continuity on the fuses, they seem okay. But as you said continuity can be misleading, ill go ahead and check voltage tonight, I brought the ignition switch into a friend of mine and he took a look at It and saw nothing inherently wrong. I thought white was the only feed wire and was stumped as to why the red wasn't connected as such, so it relieves me knowing mine isn't missing pieces. How much voltage drop is okay? I'd guess none but I could be wrong. Also any testing I do as of now might be with the engine off because my coils might be toast because I left power to them for too long and they went up in smoke! (Have yet to test them again, also the wrong ohm coils so need new ones anyways) (I could connect a 2/6 amp battery charger if that would work better than just battery.)

Forgive me if this is a massive run on message, typed up during my break with all the daily thoughts of what could fix it / testing piled into a paragraph. Also thanks for the help!

The ignition switch can be in the off position as that is a different circuit from the tail light.
A voltage drop of a couple tenths across the fuse is ok.
Remember the circuit must remain connected and be on.
White is your main, always-on feed wire to the ignition switch.
 When you turn the switch on, the brown wire feeds the blue through a fuse.  That blue wire feeds the red.

Does your tail light work in the Park position on the ignition switch?

If im checking for voltage shouldn't the ignition switch be on though since that is providing power, but continuity wouldn't matter. I don't think the running light will turn on at all in any position last time I tried it, but I will try again. The brake light does however work when either brake is applied.