First off, Welcome to GenVibe!
Disclaimer: If you order parts based on the info below and it turns out I was wrong, sorry. I've never ordered the parts, just going from what I see online
VivianVibe wrote:
What is the button called that's to the right of the gear shift on the console? (the one that covers access to shift if the transmission locks up.)
I think the full name for that little plastic piece is shift lock release button cover
I looked at mine, and a search for that part for a 2005 Matrix on one of the online toyota parts sites gave me a bunch of hits, but the picture at this link
https://parts.toyota.com/p/COVER---SHIF ... 0R020.html for Toyota part number 335540R020 looks like the one in my 03 Vibe.
VivianVibe wrote:
What are the clips called that keep the rear brake light housing in place?
If you are asking about the two reuseable plastic pins that hold the thin black plastic cover on the bottom of the high mounted brake light, those would be Toyota part number 90467-07071-22. Th 2003 Matrix parts catalog calls them "Clip, Cover" but the various places on line that google provided when I searched for that part number seemed to call them variations of Bumper Cover Push Type Retainer Fastener Pins.
There's a reasonable chance that those same things are used to hold the plastic splash shields under the engine compartment, so if you only need 2 for the brake light cover, getting a few more wouldn't hurt. (I've got my splash shields held on with zip ties right now)
VivianVibe wrote:
Where can we get both of these items?
You can order these things on line from a variety of places. Sometimes the official parts stores will charge ludicrous amounts of shipping for a dollar part. If you buy them off ebay, the lowest prices including shipping are from China, which can take a month to get , so keep that in mind if you're in a hurry
You could also take the Toyota part numbers to a Toyota dealership parts department, and if they don't have them in stock they can order them for you. I don't know if that will be a reasonable cost compared to online,