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Just an update.  I successfully extracted the broken grease zerc fitting and replaced with a new grease zerc.   

Next step I jacked up the rear suspension and greased all the bolts to the shock absorbers and suspension joints on my Kymco frame.  I now have zero squeaks in the rear suspension.  What a huge difference to eliminate these annoying sounds.  No more squeaks when off road riding on my future hunts. 

Note:   T6 is the correct metric zerc fitting for my UVX 500i bike.

The gas gauge on the earliest VW Bus was a cut-off broom stick placed above the gas tank, which, itself, - excitingly - sat just just next to the engine.
The early Beetles flew along the freeway in California until the tank emptied - then you stabbed the clutch in - flipped a reserve lever - counted to 3, dumped the clutch and continued on to Disneyland ...all without spilling a drop of your Orange Julius!

Stig

I enjoyed reading your post.

To those in the past I sincerely want to thank you all for your followup support.  It has helped me greatly.    I'm just a few steps away from having this fully restored.  The motor is strong as mule.   My next todo's are greasing the suspension system and by god I'm going to get that damn gas gauge to work.  Gas gauge displays but doesn't adjust fuel levels as the tank is filled or is getting lower.   To be continued.   These tasks are actually fun projects.  My journey continues.

Some times you can ground the signal wire comming from the sender, at least this would tell you whether it is gage or sender....

Curious if I could some how use an after market sensor arm and wire into the my Kymco setup.  Is that possible?

There is another possibility I completely forgot: EMI filter front of battery box (outside of box), right front. The two harness plugs for this filter will plug together so the fan will run. Mine crapped two years ago and the filter has been bypassed ever since! Try that.

Yea, I have bypassed mine too.

Just an update.  Did a google search and this is what I found.

Here are my highlight notes:

One of the few bad things I find on my 450i is the lack of grease fittings.
1. The only two I know are the rear suspension lower pivot arm has a grease fitting on each side and that's about it.
2. Supposedly everything else is sealed. Every so often I use a can of dry lube (PB Blaster) and spray around all and any joints, get the stuff that is Ok for plastic and rubber. It dries so no dust collection afterwards, I really hit the joining parts heavy and it seems to eliminate any squeaks, I do this after washing to help get any water out from between joints and then every so often....my father always said if a little lube is good then a lot of lube is even better!!\
3. Just a guess here but sounds like a spring squeak.
    1. As I mentioned before get a can of spray dry lube and start spraying....not going to hurt anything,
    2. just stay away from the brake pads and rear disc.
    3. Spray around all the bushings especially the rubber ones.
    4. I have been doing this for years even when I had quads, no squeeks, and everything moves freely and who knows it might even stop some rust or corrosion...
4. Mine would squeak really bad and it was coming from where the A arms meet the frame. Spray the lube of your choice on each of those. Worked for mine!

After I cleaned my bike I'll be getting greasy with my UVX 500i.

Note;I still can't get the damn fuel gauge to work.  It's gotta be the contact points in the floaty rocker arm.    That gas gauge not working properly bugs the crap out of me.   Yea, I get anal.   It displays but doesn't go down from full when I'm running low on gas.

Where are the suspension grease fitting on this machine.  If anyone knows much appreciate so I can grease the suspension.  Are there any other areas like shock bushings that can be benefited with WD40 Specialist, Water Resistance Silicone Lubricant?  If so where?

There are two thermal switches: one in the engine and the other in the radiator. The one in the radiator controls the fan, the one in the engine controls the light.

Just making sure....I know you got the right one!

where on the engine is the heat sensor?  What would cause the engine sensor to turn on the warning light? 

Thanks again for sharing your knowledge.