I've been doing Tibetan style concentration practices, zhiné in Tibetan, equivalent to samatha.

The instructions I've been given talk about 'subtle excitation', where the monkey mind is jumping around a little bit, maybe as a background process while the object of meditation is in the foreground.

I can attain what this community would call jhana by first getting to that state where subtle excitation is my only enemy, then calming the monkey by holding the object very gently, like you'd hold a snowflake, looking at it and experiencing it like silk on your fingertips (rather than forcing the mind onto it, which only increases excitation).

I was doing this on Sept 25 and realised that the subtle excitation is generated by something I do, something I can therefore stop doing, a type of neediness/clinging/clenching that is too subtle to be noticed without meditation. Then yesterday (i.e. 12 days after that experience, with daily sitting practice in those days), I got to that state again, and I unclenched the clench again, but this time more perfectly, more purely. This led to pretty complete cessation of thinking (I mean monkey-mind thinking, the sort of thinking that's formulated in words/images) that was less forceful than what I'm used to, happened more gently/calmly/naturally.

Maybe it was second jhana because second jhana is described as like first but less forceful? It's been 18 hours or so since this sit, and the mind seems considerably less turbulent altogether, with thoughts being generated either in less quantity or with less of that sort of karmic desperation.

Im not sure but you might be right. In the early stages there is more effort, urge to do stuff meditative is more there and mind chatter is gross and right in your face. In later states/stages the meditation/mind is more fluid, unforced, unefforted, as you say mind chatter ceassed or for some it falls far into the background, only leving this sense of a "watcher" in calm awareness. Maybe watch the Feeling Tone. How does it feel? Go into that feeling, is it pleasant, who is this one that is feeling it as pleasant, where is this pleasantness located, how does it relate to the inbreathing and how with the outbreathing etc ... check out that Jhanic environment as if you own it, be curious about it. Do some Insight practice in that environment. If you are where you think you are it shuld be easy seeing all sorts of stuff with much clarity.

Im no expert but just sharing my view on this  

Best wishes!