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The solenoid has a pull in coil that draws a fare amount of amps. It holds the pawl of the overdrive up against the balk ring. When you let off the throttle to shift, the solenoid and pawl advance in to the gear plate for overdrive mode and the solenoid changes over to a lower amp holding coil through a points contact at the fully engaged position.
The pull in coil will likely affect the ammeter reading but the voltage regulator should compensate for the extra current draw and give a normal reading pretty quick. Once the solenoid completes the shift, the current load should be lower for the holding mode than it was for the pull in mode and the ammeter should give a normal reading.
I'd check for battery condition or condition of battery cables first. Then check the generator and VR connections. Any problems there will affect you generator charging system. If everything there is normal then a person may want to remove the solenoid and check its internal condition. The points may need to be cleaned.