Why will the VAR signal be amplitude modulated?
In a CVOR the VAR signal is the AM one. The ground station doesn't transmit an AM signal. It transmits the centre frequency at a constant amplitude but transmitted using a directional antenna which is rotated. The result is an RF beam rather like a lighthouse beam. As the beam rotates towards you the RF fieldstrength goes up and reaches a peak then falls away as it moves away from you. The rising and falling fieldstrength appears to the Receiver to be an amplitude modulated signal. Rotate the beam at 30Hz and you get 30Hz AM. There will also be a doppler FM component on that signal because it is moving towards you and away but the AM detector in the receiver can easily ignore that. For CVOR the REF signal is the FM modulated one. The ground station transmits the signal already modulated from an omni directional aerial.
In a DVOR they swop around. The REF signal is the AM one and the ground station transmits the modulated carrier from an omni directional aerial. The VAR signal is the FM modulated one. In this case the sideband signal is rotated and the doppler effect means that it appears to the receiver as having a frequency modulation.