Non-intrusive Detection of Power On/Off for a Piece of Instrument
You could simply add some current sensing (see: current transformers, or hall effect sensors) to the power cord of the spectrometer. 

Also, popular with the "let's screw something onto our household appliance" tinkerers: Check whether some "power on" LED is on; typically, you can do that e.g. with a photodiode taped onto it. By the way, in a pinch, an LED of the same color can act as photodiode, too.

Other options include: microphone in way of the fan (assuming your spectrometer has something like that), followed by a simple RC high-pass filter, opamp or simple transistor amplifier, rectification through a diode.