The Borg Warner overdrive system momentarily kills the engine via the coil power connection when you hit the kick down switch for passing and such. This function is provided at the kick down switch initially and then the ground path is interrupted by the main solenoid when it drops out of overdrive. The system need this momentary function to allow a clean drop out and it should only be about a split second in actual operation. If there is a problem with the kick down wiring, the kick down switch, or the solenoid internal switching then this could be where the problem lies.
You should look for one of the on line diagrams for the Borg Warner R10 electric overdrive. More than a few manufactures used them. My source is from the 1949 thru 51 Mercury/Lincoln Overhaul Manual.