Trying to understand this oscillator... there's no emitter grounding or bias
My guess is that you have the Base and Emitter swapped over. Here's an example that is similar to yours. Note how inductor L3 is connected (through R5) to the Emitter, and the erase head is connected from ground (through R3) to the Base.

 

The circuit is based on a Common Collector Colpitts oscillator. The erase head in combination with C6 and C7 form a tuned circuit. The tap between the two capacitors lowers the impedance on the Emitter side, providing the power gain and positive feedback required to make it oscillate.