Definitely a strange way of doing things by having 2 separate power feeds. From what I see online, there were upgrades to the old MagneTek converters because they were only single stage converters and weren't all that great.
Anyway, I will guess at what is happening using my electronic tech knowledge and power supplies.
The one solid voltage measurement is probably the one connected to the battery. The battery will load down the charge voltage and filter it basically so it is a smooth waveform hence the nice constant voltage reading.
The other line feeding 12 volt items looks like it is unfiltered and possibly the converter is throwing out a sawtooth or other waveform that is not a nice smooth filtered one. An unfiltered voltage will basically jump up much higher than its target value and then back down. This would easily be seen with a scope which most people don't have access to.
Ok, this "sawtooth" waveform will jump to some upper value which in your case is around 18 volts. Most meters will read these spikes and give you a reading closer to what the spikes are reaching. So why does it drop when something is turned on? Because you now have "loaded" down the circuit causing the spikes to greatly subside.
Many cheap battery chargers just throw out pulses to charge batteries. This is for any type charger not RV related. When you connect the battery the pulses will smooth out and the voltage reading will drop to around normal.
One of the things I noticed was a warning on one of the labels to not connect a capacitive load to the output. This tells me the output is pulsed because if you connect a capacitor to a pulsed voltage it will smooth it out but it smooths it out at the peak value of the pulses (until loaded a bunch). So if the pulses go up to 20 volts and you connect a capacitor to it, you will get a nice smooth 20 volts. Not good in an RV.
Sorry about all the electronic theory. I cannot help myself. It just comes leaking out of my brain since I dealt in it for over 45 years.
So, what should you do? If it were me I would chuck all the old tech there and install a modern converter with a fuse panel that connects everything to one voltage feed. There is no reason to have 2 separate 12 volt sections.
Your SeeLevel system, if connected to this pulsating voltage, will not appreciate that environment as you can see by it going nuts. A quick bypass to your problem is to leave a load on the pulsating line to smooth it out. Kind of a waste of power though. It may not take much of a load to smooth it out.