I make estimated payments all the time for CA taxes and estimates without entering a phone number anywhere but the personal info area...they dont want a cell phone though, it always seems to prompt for a work number for any CA direct debits, so I stick the cell phone number in all the phone number boxes!

Ive never done them for a non resident though, are you scheduling them on the 540ES worksheet or from the Fed Info worksheets and they show up individually in the EFCenter?  I dont think they work right from the EFcenter.

If all else fails, go to the FTB WebPay website and you can schedule them right there.