I encountered one case of the tower shaft failing (shearing) - the test cell operator was making the first start of a preserved engine. The preservative oil started to burn in the LPT or tailpipe - he shutdown but the residual oil was still burning (smoky too) so he hit the starter again before the core had stopped. The impact load sheared the shaft.
At that point we had very strange symptoms - can you guess what they were?
Clue: the N2 tach is driven by the gearbox.