No man it's not the pump, and not the alternator probably. I'm 99% sure it's your stepper motor....VERY common problem! But easy.
Go to
www.ftooc.org and visit the forum....make a search for stepper motor, or idle speed control, and you'll get an infinity of info and links on how to test, clean, or replace the stepper motor. Very easy job and just takes a couple of minutes ;-)
Should you have to replace it visit
http://www.camskill.co.uk/products.php?plid=m3b0s9p362
These are FTO specialists and their contact is a must for any FTO owner...btw my user name on the ftooc site is KEN.