What are some more formal synonyms in the form of a verb, preferably one word? thesarus.com produced 'strike', but it is transitive and sounds too grating. 'Arrive' sounds noncontextual.
It occurs to me that 'occurs' is the word that you are looking for.
What about "I hit on an idea"?
Consider Materialize / Materialise or transpire.
The idea materialized in my mind whilst I was talking to a customer.
How can the average person hope to know what thoughts transpired in Einsteins brilliant mind.