It doesn't come on all the time, just sporadically. So I'm thinking I have a loose connection somewhere. Any clues on where to look?

I am having the same problem also, except both my abs and my parking brake light comes on at the same time, I have a 2001 Chevy Suburban.

i would suggest getting the codes looked up first as there are several possibilities on both for those lamps to come on.
most of the ones i have seen on the z71 are due to a front hub bearing going bad and causing it to set a speed sensor fault on the suspect wheel.

I have a 2001 Silverado and I have the exact same problem. I was told that the brake system does not have codes. A couple of years ago my abs light only came on and it was my wheel bearing. I ended up having to replace both of my front bearings. I would caution you to check your bearings. They are sealed and prone to failure from what I have heard. If one goes out completely, your wheel can fall off.
Now my abs and E brake both come on randomly for no reason. I have been told that the abs light only con mean that your alternator is getting weak. I have not been able to tell what is going on with my lights currently though. If anyone has experience with this it sounds like there are a few of us that would like to hear from you.

IF yall are willing to come to Mesquite i have a factory tech2 for gm vehicles that will read the codes if they are set and are tell us what is going on with your vehicles.

I would, but the ABS light is not coming on as much, if at all. The alternator going bad is something I had not thought of. I might have it checked. BTW, AutoZone cannot read the codes for ABS problems.

I know the ABS sensors are located in the front wheel bearings, but again, I would expect tha ABS light to be on constantly, not intermittly.

well just an fyi,when the bearing start to get some play in them the sensors will read erratically and cause a light to come on intermittently,there is also another thing that the 4wd folks can check and that is the wiring harness where it goes to the hub to make sure you have not ripped it from the retainers and are rubbing on metal.My offer stands to put my scanner on your trucks if you decide you want to come to mesquite,just call me ok.214-538-9071 cell