Can’t find replacement to this broken gear shifter. Help me not throw away this bike

TLDR: Gear shifter broke. No spare parts to be found. How to fix my bike?

I have recently bought a used bike for super cheap. I just need it to commute to work for a few months before my contract ends so anything works.

Unfortunately, right as I started riding, the gear shifter snapped, and the bike is now stuck in the highest gear. Since my commute includes a steep uphill road, it's too inconvenient to use right now.

I checked the various components and realised that the shifter is completely broken inside, but the gearbox seems okay.

So, I rightfully went to a spare parts reseller to find this piece, and I got struck by the reality that I have bought myself a very old, rare, and obscure type of bike, which mounts a Sturmey Archer 5-gear thumb shifter with double cable and integrated gear hub (sorry if I'm not using the technical terms).

The thing is, I have tried a few bike shops and none of them have the spare part, nor was I able to find it online. In fact, I haven't found any store willing to give any type of repair to my bike.

The best solution for me right now would just be to throw it away (as some bike mechanics have told me to) and just accept defeat and buy a new one. However, since everything else in this bike is working, except for the shifter, I'd like to know if there is any way to salvage it.

My question is: if I'm not able to find the spare part, is there any alternative way to completely replace the shifting mechanism? For example, I was thinking of taking away the shifter completely and using the bike stuck in one comfortable gear. Or does anyone have any suggestions as to any repairs I can give it instead of throwing it in the dump?