On 737 it is normal when leaving the aircraft unattended to have Batt Sw off & Gnd Pwr in use. Then, when the GP is disconnected (or becomes accidentally disconnected) no need to do anything to avoid arriving in the morning to find a flat Batt.
Anyway,forget all this switchology discussion, all said & done, TAWS is there to save you if all the rest goes wrong, not to enable/facilitate you fooling around below MSA in the mountains in cr@p wx.
Without wishing to prejudge, I think the cause is going to be a whole lot simpler than anything technology based.