https://youtu.be/1DfxKqt4CLY

Here's a video of my way of running a SOX 18 on a standard 15w fluorescent lamp ballast. It ignites in 2 tries by paralleling a capacitor to the lamp. This can be done with a manual switch, but i'm using a fluorescent lamp starter to automate that process.
How it exactly works, i'm not yet sure. It appears that the capacitor together with the ballast's inductance creates some ringing at 300Hz, causing a 'ring' every half period when the lamp extinguishes. It's somewhat hard to measure - because i don't have a storage scope and the lamp will ignite fairly rapidly.
It works very well, ever so slightly under-running the lamp with a measured 310mA of lamp current (which is rated for 350). Measured with a conventional multimeter, not accounting for wave form etc.
Without the capacitor, it takes about 20 kicks from the starter to finally get it lit. It does not work well without.

By now i also own a Philips XGC113 wall/ceiling light with a normal ignitor and ballast.

You are better off using a 20W ballast because a 15W T8 lamp only runs at 300mA and an 18W SOX low pressure sodium lamp runs at 350mA, which is closer to that of a 20W T12 lamp, but this only works if the magnetic ballast has an open circuit voltage of around 200V or so as I have been unsuccessful on 120V series choke ballasts since the 120V open circuit voltage was insufficient for the lamp to initiate an arc.

This is what i had sitting around. 18w fluorescent ballasts exist, but i couldn't find a local shop that sells them. Just found out a SOX-E (specifically the E, datasheet from the late 2010s) is specced at 57v 330mA which is close enough to the 310 i measured.
I was already looking for the real stuff, humming and hawwing over the ~70 euro that an original ignitor, base and ballast would cost me, when i got offered a complete wall light for free

This is running on 230v, on 120v it would be much harder to get it to ignite at all. Building a parallel resonant LC circuit with another ballast and capacitor parallel to the lamp will massively make the voltage swing up. Would be an interesting little test but definitely a risky affair, unloaded the resonance will make it rise well past the voltage rating of any reasonable capacitor. But i think i'm gonna try it anyway for the Americans who suffer from a 'voltage deficiency' so to speak. Though i guess you could run the stuff on a 240v split phase outlet.

If anyone needs anything SOX related, check out this shop: https://voorraad.dbl-verlichting.nl/products/exc-voor-sox-e-18w

I have also been able to use a 277V North American 15W-20W preheat fluorescent tube series choke ballast and some North American FS4 fluorescent starters in conjunction with a 120V to 277V step up transformer to get a 277V supply as a workaround for the low 120V OCV difficulties I struggled with.

See here:

https://www.lighting-gallery.net/gallery/displayimage.php?album=search&cat=0&pos=5&pid=209007