Sometimes when I turn the key to start, it will make a little click but doesn't crank. The clock and dome light will go out, then come back on when I release the key. I'll have to try it several times and then the car will finally crank and start.
Sometimes it doesn't do that at all.
Everything else works fine...is this a sign my ignition cylinder is going out, or just some screwed up wiring?
Probably your ignition switch (not the cylinder). It's common for them to go bad in these cars.
Is there a writeup or FAQ on replacement? I want to see what all is involved, because I need to do it before too long.
It's not a bad job. There are two Torx bolts in the steering column that hold it in. I can't remember what else is involved.
If you have a set of security torx bits it's really simple.
Here's a replacement in a Mark VII.
http://www.thelincolnmarkviiclub.org/documents/tech/1984ignitionSwitch.pdf
AFIK the dome light is totally independent of the ign SW, I'd be looking for a bad battery cable or ground...
Could have a bad cell in the battery...
A short in the ign switch circuit that pulls enough current to kill the dome light, is going to cause smoke...