Here's the thing, some widebands are sensitive to voltage supply. The Innovate widebands are, at least. That means you can use a switched power source for a relay, but the actual power should be from a source like the positive terminal in the engine bay. It's been a while, but when I wired a wideband in my Camaro, it crapped out after a couple months. Killed a sensor or two, kept acting up, etc. Replaced the gauge and controller and had the same problem, turns out it was my 12V supply. I used the same Innovate LC-2 in my Hombre swap and it's been working flawlessly for 8500 miles so far, road trips, daily service, etc. Just make sure you find out what NOT to wire it to from the manufacturer and abide.
1957 Chevy 210 Belair Wagon LS3/4L80e
2005 Pontiac GTO LS2/4L65e
2014 Chevy SS 6L80e