My wife has a 2004 Thunderbird that she absolutely loves. Honestly, I think she would get rid of me before the car. I want restore the inside and outside of the light cover. What has other people done? Have you replaced both of headlight covers or have you been able to clean it so it looks good as new? Thank you.
		
		
	 
The 
headlights are complete units, so there is no "cover" to restore, and you can't get to the inside without destroying the 
headlights.  Even if you clean up the outside of the units, at this age the yellowing is in the plastic clear through.  They may also have tiny cracks throughout the volume of the plastic and there's no remedy for that.  My own 2005 Thunderbird had the same issues with the 
headlights.
You CAN make them look new 
by buying replacements.  I found them from  Ford for about $600, but they are also available as 
aftermarket replacements. They look great, fit perfectly, and adjust exactly like the factory units .  Since there are no tiny cracks robbing light, they are much brighter than the old ones  I recommend buying replacements instead of trying to polish up the old ones.
Your manual covers 
headlight bulb replacement, and the same process applies to replace the entire unit, since you have to pull them to get at the bulb.  It takes a wrench to remove one nut (I think it's a 10 or 12 mm) and a pair of long pliers to grab the two spring clips on each 
headlight.  You'll also need a small (I think 5 or 6 mm) wrench to turn the height adjustment after replacement,  That adjustment is also in the manual.