Sorry fellas... I'll take a look at the "whatsit" (lol) again when I get off work this evening. It really is a whatsit because the loose leaf instruction book in the kit doesn't seem to mention it at all.

It is entirely possible that it isn't a relay and that instead its just a fancy-pants capacitor to keep the bulb out indicator from glowing. However, my bulb out indicator didnt glow with the kit installed by itself either.