as i understand this gypsy rondo:entire A section = 16 measures
then, we have the gypsy element. you go from a D major sound to a C major sound suddenly (excepting the G# - which also brings in a bit of an a minor sound at the same time). anyways - you notice the peculiar C natural - which seems a bit odd if there is no C# in the key signature. so - go with the flow and call it VI or vi (sort of pentatonic sound - C D E F#G#). and the little bridge brings it back into G major with the 1/2 step accidental suddenly cancelled again. the gypsies liked to play with chromaticism. so that's the gypsy element. just doing something you're not supposed to with the harmony. a sort of magic trick.
"now - to properly analyze you have to count all the measures and refer to measure numbers when you speak of cadences. .....in the B, C, whatever."
an intro m. 17-34 is typical of another section in the dominant
expo - in some strange way - i see the piece actually starting at the first 'minore' section after being introduced slightly earlier in the introduction at m 35.
now, that i think about it. skip the idea of the intro and just start the rondo with the idea that it starts at the expo directly and that it returns at m 144 at the 'maggiore' section. or, keep the idea that the introduction is there - and assume that he was being creative when he recapulates on the themes of the introduction INSTEAD of the themes from 'intro.' (that's my best bet!)so - you have in effect - a rondo form superimposed upon a sonata form (without intro- necessarily)
just think of haydn as ADHD. you'll get it as soon as you just 'go with the flow.' he adds a coda to the end of his rondo and an intro to the beginning. also, he delays cadences wherever he can. so if you take a ruler and try to measure equal 8 measure phrases - you'll end up stabbing yourself with a pencil out of frustration. i think the 'introduction' is where he introduces all kinds of themes and ideas to get for both A and B C D themes throughout the rondo. after you analyze the big stuff - look at the motives he starts using and highlight them from the intro -to whatever place they are used (with different color pencil).as i see it - the 'intro' is the entire section up to the minore section.if you look at the minore section as the true beginning - you see a gypsy step out onto the stage and play with all his guts. look at the fz's that begin the entire start of the minore section.what haydn is doing is STARTING the rondo - (not with 'intro' - but he recaps to it) with a variation. surprise! haydn is full of surprises.