The printed Owner's Manual had a serious omission (it doesn't say that the trip odo has to be set to the "A" setting before stopping the engine, and still doesn't make it clear that you don't actually restart the engine. There is a correction at toyotaownersonline.com, but it is incomplete.
The procedure that worked for me (2008 Highlander LTD, non-hybrid, with smart key system and multi-information display):
Step 1: With engine running, set trip odometer to "A" setting. Stop Engine.
Step 2: Press and continue to hold trip odometer button in.
Step 3: Still holding trip odometer button in, do NOT press brake peddle (i.e. do NOT restart the engine), Press START STOP button TWICE. This is what the manual calls the "ON MODE," (see printed manual164) "All electrical components can now be used."
Step 4: Keep pushing the trip odometer button in until the word "COMPLETE" appears in the multi information display.
If you actually start the engine in Step 3 the display shows the reset starting, but it stops before it is complete and the Oil Maintenance Required Display does not go away. Likewise, if the trip odometer is in "B" or total mileage setting then nothing at all happens.