How do I take the "stringray" emblem off the side of the fenders of my 74.  I want to detail the paint behind them.

Steve, unless you're repainting the car, or replacing the emblems because of damage, I wouldn't recommend removing them. They are held on with two-sided tape, and can be hard to get off without damaging the paint.
The studs are just to position them, not to hold them on.

If you want to remove them, get some 3M "General Purpose Adhesive Remover", pt# 051135-08984. This will release most of the "sticky" from the tape, and allow you to gently pull the emblems off. Be carefull not to let the remover stay on the paint very long, as it can discolor it. Then, you'll have the problem of how to put them back on!

New emblems have the tape already on them, but used ones, well, you're on your own there! I have used regular two-sided emblem tape, and spent a couple of hours cutting it to fit the backside of the emblems. Not a fun job, I might add.

Best thing is to leave them on, and work around them. Use a very soft bristle toothbrush, or get a camel-hair paintbrush(detail brush), to work the dried wax/dirt out of the emblems.

What's the best way to clean the crossed-flag emblems?  Mine look faded, but I'm not sure if it's built up gook or if they need to be repainted. 

[QUOTE=kkfinch] What's the best way to clean the crossed-flag emblems?  Mine look faded, but I'm not sure if it's built up gook or if they need to be repainted. 

[/QUOTE]

Soapy water and a soft bristle brush. The enamel on the emblems can fade over the years, and look dull/dingy. They can be repainted, if you have the patience, a steady hand, and the correct red color.

I remove factory emblems mounted with double sided tape with fishing line.  Just work the fishing line up and down as you go across behind the emblem and after the emblem is off you can clean up the tape on the car with ease.  Bob

thanks for all the info everyone.  I would have never had guess the tape held them on:  neat trick with the fishing line.  Guess I will try the soft toothbrush first. 

I popped mine off with a small screwdriver very carefully. However I am in the process of painting the car. They came off fairly easy. To put them on I'm thinking about puttin retainer nuts on the back side of the guide pins.

I've had success using dental floss in the same way carfun uses fishing line.  It is strong and easier to get into tight places.

I read this post thinking,.... interesting reading, I'll need to know this someday. Well cleaning her up this weekend and found the L-82 emblem on my passenger side almost completely hanging off! Not sure if someone was trying to steal it or what. So now I need to figure out how to get some two sided tape on this emblem and looking neat. I guess glue is not a good choice?

I don't know how yours are put on, mine have holes in the body with tits on the emblem themselves so I can use the two sided  tape and/or speed nuts on the tits.