Upon a quick inspection, this is a moderate-light used FE2. The exterior is a bit banged up (esp on the bottom) due to not using a protective shell. The viewfinder is full of black clunks (from disintegrated rubber). On the other hand the shutter is very crisp and responsive, the crank is light, the lightmeter (center weight) is pretty much spot on. The lens is well oiled and precise. However, like most old SLRs, the rubber parts are mostly disintegrated. This includes the mirror damper, which is one of the first parts to disintegrate on all SLR cameras. Next to disintegrate are the light seals and cloth seals around the film container.
First, the clean up process, using solvents. What you see above the mirror is disintegrated goo-gunk instead of a mirror damper. Over 2 decades of oxidation, heat, humidity does this to the mirror damper. It'll happen to your most modern 2009 SLR as well! Just give a decade or two, it'll happen. If you're going to clean it up, you can use the liquid lighter (give ample room for breathing), or if you're careful, alcohol is acceptable too but DO NOT USE ALCOHOL ON THE VIEW FINDER! It will smear it permanently and you'll have to get a new one.
This is how you clean the mirror damper/rubber. Just rub it off using a bunch of Q-tips and eventually it'll look something like this.
Now to get a new mirror damper-- slice off a piece of mirror damper. Interslice provides dimensions with detailed instructions here: http://www.kyphoto.com/classics/sealreplacement.html
This is what it should look like when you've cleaned up the mirror damper. By the way, this is an excellent time to pop-off the focusing screen so that you can clean up the junk around to make the view finder nice and clean again. Make sure to not rub against the screen or else it'll scratch easily. Also, make sure you know which side of the focusing screen you're mounting on as the side matters for focusing accuracy.
This is what a mounted mirror damper should look like. By this time, all the black gunk from the mirror and focusing screen should be cleaned up. I also replaced the light seals in the back of the film container. Now to test it-- use your ear! If it sounds good, it's good. The FE2s have a click-snap sound. Unlike the sluggist Minolta shutter (sounds like thut-swoooosh-clip), the FE2 sounds crisp. Precise. You know a good Nikon titanium shutter when you hear one.