This is kind of a multi-part question: 
1) Is there an open-source implementation of something similar to
google suggest javascript code that can be used without special server
side requirements (other than php/mysql which I have)? It doesn't
necessarily have to be as powerful as Google's own code.  If so, where
might I find the code?
2) If not: other than using a frame, is there any new fancy
DHTML/Javascript/PHP way of having one part of the browser screen
update itself with information pulled from a database (returning
results of a search box for example)?  I'm creating a timeline
database and when adding new events, I want to give the user the
opportunity to associate the event with a person or multiple in the
people database.  They should be able to search the database for a
person to connect the event to but I would prefer not to have the page
reload completely every time they search for a person.  Nor do I want,
ideally, to have to dump the enter contents of the "people" database
table into a checkbox list or listbox.  Any ideas?

ANSWER!!

Question #1: yes.. 
This is a step by step break down of exactly-very similiar how google
suggest works with a database/array entry.

http://www.nsftools.com/tips/ZipLookupTest.htm

Question# 2: yes .. and no.
There are multiple solutions to this. 
One way of doing this is if the entire content can be loaded into
client side memory.. ie. its not that much you can use dhtml and css
sheets and javascript to reorder the text on the screen without
reloading the screen

The other option is if you have to re access the dataabse you use an
iframe. Its not a frame but similar to one.. you can collapse/hide the
iframe on all sorts of actions.

One site that uses iframes very nicely is www.k10k.net

Take a look around.. 

Also another interesting place to visit is www.brainjar.com and look
at his step by step dhtml and css examples..

Hi there, good enough for me, for the time being, go ahead and post it as an answer.