I got the following from some Afrikaans etymologists/lexicographers ... so it's reliable, if not helpful:
Sita, met variant
Zita, kan blykbaar 'n Persiese naam wees wat 'maagd' beteken, of 'n Etruskiese naam wat 'jong meisie' beteken. Verder is daar ook 'n moontlikheid dat dit van Spaans kom, en 'rosie' beteken, of dit is 'n Franse naam wat 'slaapkamer' beteken.
Ek kan nie iets kry wat 'n aanduiding is dat dit 'n ingekorte naam is, bv. van iets soos
Rosita, ens. nie.
And the translation:
Sita, variation
Zita, can apparently be a Persian name meaning 'virgin', or an Etruscan name meaning 'young girl'. It is also possible that it might come from Spanish and mean 'little rose'; or it could mean 'bedroom' in French. I can find no suggestion that it is a short form of a name like
Rosita etc.
As you can see, the learned gentlemen didn't pause to consider that they are spelling it
Sita instead of Sieta ... usually I'd be able to track down a real, live Dutch informant, but not today!
Anyway, hope it helps to narrow things down.