Goood morning, welcome to JustAnswer!. This is Ed.
Even with the great information you've sent, I can't know exactly where the problem lies, but if you want to skip ahead... I'll suggest that it's the combination (combo) flasher unit if all bulbs have already been checked or replaced. We'll see.
The circuit begins with the underhood Power Distribution Center (PDC) at Fuse 4, which is a 20 amp mini-type unit. This powers your brake lamp circuit.
Since rear lighting on your 2000 van uses just one bulb for both brake and signals, some trickery has to happen to the stop lamp switch output to interrupt brake lamp signal output and make the bulb flash when signaling and pressing on the brake.
That would be the combination flasher, located under the left end panel of the dash. Look for a blue or green colored "cube" for identification.
The turn switch receives power from the ignition switch (for signals) and a direct battery feed for the 4-way flashers. If your rear bulbs work and flash with the 4-ways on, it demonstrates good circuit operation and bulbs all the way from the switch to ground. Since your front signals work, we can safely assume that your key-on feed is OK... it's also used for rear lamp operation, but through different legs of the signal switch.
Let's start by checking the 4-ways. Do they light up in the rear?
How about the center brake light -- the one up near the roof? This circuit is a direct output from the brake switch (although it runs through a fuse in the interior panel) and isn't influenced by the flasher unit. If the 3rd brake light works, it at least shows that you have power to the brake switch. Keep in mind that the 3rd brake light is often overlooked and bulbs may just be burned out. It takes two #921 bulbs.
Grounding for your brake/ signal, park, license and backup bulb filaments are shared, so this would be a good time to check the rest of the group for operation. A weak ground may support park lamp filaments, but suddenly become overwhelmed when a stronger voltage signal to the other filaments are sent. If you have park lamp operation at first, but everything dims or goes out when the brake/ backup circuit is engaged, you almost certainly have a bad ground. Let me know.
While your turn signal switch could technically be the problem, it would have to lose two separate electrical legs for both rear brake/ signal bulbs to be out. I figure it's most likely to be a single source, the combo flasher.
Locate the flahser, turn the signals on (key on of course) and start wiggling or remove-install the flasher unit. It just pulls out of the board.
They often have internal electrical breaks that respond favorably to this sort of action and momentary recovery of the signals and brakes may happen. If so, you know how to fix it, provided the contacts in the fuse block are in good shape.
Expect it to set you back about $40-$60, depending where you buy it. I'd expect an aftermarket flasher to be a bit more economical.
Check it out and let me know if you have any problems. Thanks!