Mysterious nerve shooting pain inside gum where is no more teeth left?

Hi. First sorry my bad english, as it not my home languange. I try to explain my situation. all my left upper tooth is so bad condition that i plan to extract them all and made a denture eventually. So 8 month ago i sensed some shooting nerve pain in arround my left upper eye tooth.(that already had multiple cavity) This sooting pain is coming randomly, and the worst thing that i cant know when to happening next. So i extracted this teeth and this shooting pain stopped immediatly. 3months later this shooting pain come back again from nowhere, at the same spot , and happening again multiple time in a day. In that upper left area there are only 2 tooth remained in a bad shaped so i extracted them (plan to make a full denture as i said). I hoped that one of this tooth is the source of the pain. But not. Shooting pain continues and there is not a single tooth left that side. !!!

So this sharp pain as I sense is coming from deeply inside the gum. It is localized. I can pinpoint that exact location. If i touch and press this point i can trigger it immediatly until i done pressing it. So the pain is not the worst thing, the worst is that is shooting randomly only for a milisecond, at random time. Doesnt matter what i do eat, or drink, or do nothing, this shootings is totally random. It feels like a tooth nerve is inside a gum and irritated, but not a single tooth remained that area. I think its importat that sometime this shootings is pulsating with my pulse. I suffering from this around 8 month . There is 3 month time when this shootings suddenly stopped then i almost forgotted it, and suddenly come back then 4-5 days agony it stopped for 2-3 months then now happening again.

.So i visited dentist multiple time, take a 3D X ray scan an nothing to see that area. So next is booked an appointment to oral surgeon and he is cutted my gum and cleaned everything, he sad he didn’t saw any inflamation, and the clean didn’t hurt all. After I went home and 2 hours the anasthesia effect worn out, the shootings came back. This is my situation now. Where to next?

My questionis do you have tips what can this it be?

I already learned about [Trigeminal neuralgia]but i dont think that is the case. This is not as bad as i read TM is, and my pain is always localiced in that one place inside the gum, from the beginning.

Thanks for you answers.