Most of those early single transistor circuits are blocking oscillator type
http://www.lighting-gallery.net/gallery/displayimage.php?album=2942&pos=10&pid=57299Maybe with some differences and more components in the feedback and supply, which would make it better than the basic 3 component version
We gotta know what are the inputs/outputs on the transformer (coil sets, taps, roughly how many turns) and the battery voltage