I looked at the repair manual for the '04 LS430 and it doesn't offer any diagrams or repair info on the internals of the mirrors. It only gives a test procedure and if the mirror behaves like yours does it say to replace the entire mirror assembly.
Your options are:
1) Manually move it to driving position and leave it alone (turn off auto mirror switch)
2) Get adventurous and disassemble the mirror and see if it is something obvious like a micro switch that tells computer unit to stop motor when it gets to driving position.
3) Get a new one from on line parts outlet (Champion Toyota is $609.25, parts.com is $495.55 for p/n 8794050432c0 2004 ls430)
4) Try a used parts dealer like
http://www.specializedpartsplanet.com/