Transformer doesn't have 2 x continuity
In a standard transformer, you'd expect there to be continuity on both sides.

For years now, things sold as 'transformers' for 12v lighting have been SMPS systems. This is mainly for cost. The old style iron transformer is expensive and heavy. It's cheaper to use some electronics round a small high frequency ferrite transformer to drive low voltage lighting, even at the 50 watt level. 

The first thing the input terminals see is a bridge rectifier, so you're not going to see anything at all below 1.4v. Once above that, little more than leakage until, depending on design, the thing decides there's enough input voltage to start turning on.

Something like this is typical, 35-105 VA, constant output voltage, £5.