If you have owned a 1997-2005 GM minivan you are well aware that their electrical systems leave much to be desired. One of the main issues you'll find is that the brake lights, tail lights, marker lights, turn signals, and backup lights have a mind of their own. It's not really their fault, but GM was cheap and this leads to other components failing. A common problem is that the turn signals won't blink, or they'll blink too fast, or they won't work at all. Other problems like brake lights not working and backup lights coming on with the turn signals can get you a ticket pretty quick. I got pulled over myself for this issue. My reverse lights were blinking INSTEAD of my turn signals when my right turn signal was on and the brake was depressed. With the brake released, they operate normally. This is how I got out of the ticket, while seated in his cruiser, the trooper noticed they work fine if my brakes aren't on. Said to get it looked at. Anyway, these problems can come from a number of sources.
1) Any light bulb being burned out anywhere on the car.
I know it sounds odd, but if the right front marker light is burned out, for example, neither turn signal will work well and the brake lights will be very dim with the lights are on. If a brake light anywhere is burned out, it can cause the markers up front to go off when the brake is depressed. There are a million problems it can have and the change in resistance from a burned out bulb wreaks havoc with the whole system. Replace bulbs IMMEDIATELY when they fail to avoid further problems.
2) Bad tail light circuit board.
This plastic socket, similar in size and shape to a surge protector, houses the 4 light bulbs in each tail light housing. It has a circuit board inside which controls the flow of electricity from the 6-pin connector up top down to the bulbs themselves so that the right light blinks or lights up. If that board gets dirty, wet, cracks, or melts, it will cause problems. Thankfully these are cheap, you can buy them for about $12 each on Amazon, or $21 at RockAuto, or $40-$50 at local auto parts stores like AutoZone or O'Reilly.
3) Melted connector at tail light circuit board.
While you are checking the circuit board for proper function, keep in mind that moisture and dirt and other problems will place a bad load on the electrical system. This can cause problems elsewhere in the circuit, starting with, and most commonly, the PT246 6-pin connector at the top of the circuit board. If the board has a melted pin, this connector will have a melted pin, so replace them together. Here is the one on my van's right taillight:
Thankfully they are cheap to replace as well.
4) Bad multifunction switch.
If all the bulbs in the system are known to be good, there are no ground faults, the circuit board and connectors have been ruled out, and there is still a light problem, then the multifunction switch may be to blame. This is basically your turn signal, cruise control, and windshield wiper stalk on the left side of the steering column. The entire switch surrounds the steering shaft and also includes the hazard warning lamp switch. If you're comfortable working around the airbag, you can remove your steering wheel and swap it out fairly quickly, especially if you have experience with these Saginaw-style tilt steering columns. This is the most common issue when the brake lights have failed. These can be found on eBay for about $120 but are much more expensive elsewhere.
5) Bad Body Control Module.
This little bugger can be the cause of problems besides your lights as well. If your courtesy lights come on randomly, or your van locks and unlocks as you're driving down the road, or your DRL's won't come on, this is something you might want to check out while you're chasing the problem. This box is located on the driver's side of the dashboard, near the steering column, above the large plastic knee panel. Ensure you get a model updated/new enough to cover the features of your van. If you have an alarm, you need revision 4. If you don't, revision 3 will do. Near this box is also the security system box so make sure you mess around with the right one or you'll get that dreaded blinking "security" light.
I hope this helps you figure out lighting issues on your van as I am chasing the same problems at the moment myself. So far I've been down roads #1 and #2 and #3. If those fail I'm going to swap BCM's and then try the multifunction switch. Then I'm going to try and program a remote fob since my loving wife ran mine over and left it in a busy intersection for an hour.