I have a casual cozy style, with solar powered dim fairy lights on the smaller shrubs and plants, with the main tree having diffused colored incandescent/LED lighting. On the inside, purely warm white incandacent fairy lights.
I have a row of 6ft to 7ft palm trees bordering my garden, and I plan each will get its own solar fairy lights. The reason I like the solar lights is because they are very cheap and will work throughout the year.

You're good! it was confusing at first but I did end up figuring it out.

@NeXe Lights
The ballast would be working harder than it is meant to. Whether or not this will happen to the point of it overheating in uncertain.

It would definitely not cause immediate damage to the ballast, so monitoring the ballasts temperature during operation is the best way to proceed. If the ballast starts getting too hot, cut the power. You almost certainly won't cause any damage to the ballast if you maintain reasonable temperatures.

Leaving this to run continuously at high temperatures for days/weeks/months on the other hand, that would probably shorten the lifespan of the ballast, possibly causing failure.

So, would running a 400W PSMH lamp on a 400W HPS ballast cause the ballast to overheat? I'm not worried about the lamp; it's a cheap Chinese-made Westinghouse lamp. I'm more concerned about damaging the ballast.

Glad to hear! Sorry I couldn't be of more assistance. I would love to see it once it is all back together!

I would have expected the same, but do not fully understand the process.  I remember from my time in making SOX lamps at GE that every day there would be a few defects from the exhaust machine with high CO2.  They were usually caused by poor connections to the four electrode leadwires, which were then not activated at the full 5.0-6.6A for the required duration.

In case of no activation of one electrode, the C02 evolution was of course huge : the lamps would strike with the correct NeAr colour, and within a few seconds turn blueish white and extinguish.  But in case of partial activation some lamps seemed to be able to run almost indefinitely with a pale purple-pinkish discharge.  Perhaps as you say the CO2 was quickly broken down, the O2 would be gettered by the sodium and hot tungsten electrodes, and the carbon deposited in solid form.  But their discharge colour remained notably different, and these lamps were easy to detect because they ran insanely hot.  Perhaps the more stable CO was formed and some quantity of that could remain?  Of course it’s also possible that if a cathode was not fully degassed there may be some residual nitrogen contamination.

We must also remember that the first cold cathode discharge tubes of Daniel McFarlane-Moore were in fact based on fillings of pure CO2 - but indeed that quickly dissociated and complex systems were required for gas purification.  Same for the original CO2 laser invented by Bell Telephone labs.  The problem of gas breakdown was not fully solved until Sylvania’s invention of the improved CO2 gas-transport laser, which quickly became the standard design.  That completely avoids dissociation of the CO2 by mixing it with helium and nitrogen, and keeping the gas continually moving at high flow rates through the high power discharge.  But none of these features exist in the small F8T5 type emergency fluorescent lamps.  I only know about their unusual gasfilling from the manufacturing specs, but could not find any patents and the people who would have developed these all retired a long time ago.

UPDATE! She lives! she works, it's alive!

The tag in my luminaire seems to look almost like this image I've provided.

I think the fixture was 240 volt when it arrived because the center terminal has a spade wire connected to it. This does have a photocell receptacle but it was never wired to the ballast and other parts for whatever reason.

Looking at the picture, I can't exactly tell what wires are going where. If you can, then that would probably be the best approach. But be careful turning it on, I personally would limit the current of it with a hairdryer or other appliance in series at first startup to make sure nothing is gonna blow up when you give it full 120.