From your description, which you want to highlight when giving the neuro your history, your tremors sound like active, not passive, tremors. Passive tremors--i.e., when, say, the hand is at rest--are associated with Parkinson's; active tremors--e.g., when trying to hold a glass of iced tea at arm's length--are often associated with essential tremors. I had nonParkinson's tremors, which may or may not have qualified as essential tremors, and they disappeared after a one-yr course of propranolol.

I get your concern about how to present to the neuro. It's a stressful transaction. Optimally, you give the neuro the facts, and the neuro analyzes them, diagnoses your condition, develops a treatment plan, and executes the treatment plan.
There's a lot of play on the neuro's side of things, so it's understandable that you may want to go beyond merely providing the facts.

Several factors must guide your decision as to whether to do more than present the facts. Prob the most important are the neuro's competence and enthusiasm. Without both, the neuro may need a nudge--sometimes, more than a nudge. At one time, you may have had a choice among neuros, but, where I live, finding a neuro is like finding an obstetrician in Idaho.

Other factors are impt. A recurring referral source, such as a nearby primary care dr or hospital, helps a lot, as the neuro doesn't want to lose future business. On a related note, how busy is the neuro at present? And how urgent are your needs?

It's a tough puzzle to solve. You can stay in your lane and hope for the best or you can go for the gold by "oversharing" with your analysis, rule-out diagnoses, and treatment parameters, even plans! I tend to wander out of my lane, at least to the extent of some analysis, but try to stay on the roadway by going no further. At the end of the day, I'd rather be frustrated that the neuro fired me than if I stuck to a presentation of the facts and got little or nothing in return. Better to have tried and failed?