Tough call! I'll float several ideas in case they might help.
Sometimes it's necessary to install diodes in logic sense lines to prevent upsetting existing circuitry, such as turn signal and 4-way hazard light blinkers. People who tow trailers run into this issue with some frequency. Those circuits can be touchy, depending upon how they're implemented, especially when a computer is involved.
It may be that the grounds on your various devices aren't all at the same potential; perhaps one has a poor connection, so the current draw of your additional electronics modulates the current path excessively, creating voltage swings.
Sometimes stereo units don't appreciate having a speaker (-) terminal grounded; it may still function, but the amplifier may oscillate at audio through inaudible ultrasonic frequencies, which can create all manner of unpredictable and hard to track down havoc. Certain older Dodge vans in particular were guilty of using the chassis as the negative conductor for the speakers! Saved a few pennies in wire... Make sure your speaker wiring is correct for the specifications of your stereo.
Make sure all of the wiring attached to the stereo has its insulation intact, no screws (like from paneling) are puncturing any of the wiring, and that none of the terminals can contact the chassis.
You may have a corroded terminal in an electrical connector in those circuits, and it was only barely passing adequate current to begin with. The new additional current may have pushed it into excessive voltage drop/instability.
I'm not certain of the physical wiring in a Chevy van, but it looks like you may have lifted out the rear light buckets? I see some water droplets running down the body, and what appears to be blue masking tape on your splices... Did you crimp or solder the splices, or are they merely twisted together? Are you sure the wires haven't punched through the tape, and that the splices you made aren't submerged or have become waterlogged? Blue masking tape adhesive may not hold up for long either; has it fallen off?
On a Dodge van, the ground for both tail lights is a single screw which is also used to hold down the passenger side tail light lens and bucket! If you have that one screw loose or missing, the tail lights on both sides will become erratic or extinguish entirely! Any electronics tied to that circuit would get quite a ride when the turn signal or hazard light blinker circuit or brake light circuit was engaged. If there is a similar single failure point common to both tail lights on your Chevy van, it might bear some close scrutiny.
Are all of the bulbs installed correctly, and the socket contacts in good condition? Sometimes a bulb can be inserted in an incorrect way in a worn socket, especially a cheap import replacement bulb, which may not meet the dimensional specifications precisely. A faulty filament in a bulb, or a bulb of the incorrect type can seriously upset things as well.
I'd try putting a voltmeter on the various wires and take some readings and see whether any of the wires exhibit a voltage change which follows the audible and visible symptoms you've observed. If possible, take all voltage readings using the same ground reference point in the van, so the readings are directly comparable.
What a beautiful campsite!
Thanks for the pictures.