Lakerat

Do caliper pivots need to be oiled or taken apart and greased periodically? Is there any other locations on calipers that need lube such as contact points for timing the caliper parts. Seems lube could cause brake calipers to pick up a lot of dirt since they get debris slung on them.

okane

Whenever I rehab an older bike I always take apart the calipers, clean them, and swab a bit of bearing grease on all the pivot points using a q-tip. Wipe off any excess. I don't use oil lest if might too easily migrate to the pads or wheel sidewalls and doesn't last as long a grease.

I imagine there are some calipers for which this is not necessary or would damage certain parts effected by petroleum based grease, but works like charm for my old school side pulls.

I don't do this as part of regular maintenance unless I got a lot of mud or debris on the caliper that might effect performance.

Andrew R Stewart 

Yes, and parts that move against each other need cleaning and lube of some form. The key is to apply a small amount, work it in and wipe off the outsides. Periodic wiping off helps prevent the build up. Andy.

NYMXer

If it moves, it needs lube. A little lube goes a long way and too much can end up on the rotor or pads. That never good because you compromise braking and the pads often squeal.
I like to use ATF fluid, or a dab of very light waterproof grease.

turkey9186

I use a single drop of Triflow on the pivot points once a month or so (depending on how often I ride that bike.)

Retro Grouch 

None is bad but it's almost impossible not to put on more than is necessary.