My car is ticking. Literally a fast paced loud tick coming from the battery, I think. Anyone know what this is all about?

Here's a few other things, on a cold start, If I put the headlights on and rev, the lights get brighter when revving and dimmer when idle. Is this an alternator problem?

What can I do to check the battery and alternator?

 

It ticks while running or it ticks while cranking?

If it ticks while you crank it, have the battery tested at an auto parts store. If the battery is okay and holds a charge, it's probably your alternator.

If it ticks while the car is running, I haven't the foggiest idea.

 

Sounds like your alternator's going.
You can get it tested for free at several auto part stores.

 

It ticks when key is in ON position, not cranking. Then it stops after 30 seconds or so. It's whenever the ignition switch is on.

Stops after it starts running, I think. Can't really hear it over the engine noise.

Still sound like the alternator?

 

could be the solenoid in the alt.
it's a simple removal just pull it and have it tested.

 

if it only ticks after you turn on the key its probably the mixture control solenoid, it controls the dancing needles which regulate the mixture. don't worry, its normal. as far as the headlights dimming out when at idle, have your battery and alt. checked but you will probably find they are OK, I found the GM alternators don't put out as much current when at idle. aside from checking your grounds and connections, it could be normal also. my car does everything you describe and I don't have any problems with it.