No, the arm that bolts to the door is a different shape and pattern.
Someone posted some time ago that they mated the power head to the 2000-2002 towing mirror arm/mount.
Send me a pm, I have some used ones that will fit your 1999, from a 2001 truck. 2000-2002 used a manual flip out towing mirror.
They will fit 1994-2002 BR series trucks.
The 03 mirror that you refer to, first appeared on the 02 DR series (1500 and light duty 2500 trucks), then it was transferred to the 03-04's.
Hope this helps.
Andy