I had feared that such was the case. I was really asking about the gacchati, for "s/he goes" and wondering why it wasn't gacchata.

Because in Sanskrit (like in other IE languages like Greek and Latin), the ending for the 3rd person singular of any of the three genders is -ti, cf. Old English -eš, Latin -Vt. In the present indicative of gam 'to go':

1st Person Singular gacchAmi
2nd Person S gacchasi
3rd Person S gacchati
1st Person Dual gacchAvas
2nd Person Dual gacchavathas
3rd Person Dual gacchavatas
1st Person Plural gacchAmas
2nd Person Plural gacchatha
3rd Person Plural gaachanti

You see something like this is the Hindi forms of hona 'to be':

hun 'I am'
hai 'thou art'
hai 'he, she, it is'
hain 'we are'
hao 'ye are'
hain 'you are'
hain 'they are'

Though, in Hindi there are less forms. But, the gender concord is on verbal adjectives and not finite verb forms.

Ceci n'est pas un seing.