Help with P0128 Error

Quack?

Hey all,
Long time Z owner (used to have a boosted 350z) - newer to this forum but I've been lurking for a bit. That said, hoping for some communal expertise to help me with this one. I threw a code a couple of months back, P0128. My initial thought was that the thermostat was stuck open, no big deal - the engine took a tiny bit too long to get to temperature every once in a while, with no real negative impacts. I bought a new one but haven't replaced it yet. That said, really funky issue this morning, which is where I'm a bit lost.

In a nutshell, as my engine was getting to temperature coming into work, within just a couple of minutes the engine temp gauge started bouncing around. I mean, all over the place. It was like watching a light on a carnival game or something - it was changing constantly. Would bounce from completely cold up a few ticks, down a tick or two, up a few, down to cold again, all the way up to normal temperature, and then around some more. This was very rapid as well - there's NO way the actual engine temperature was bouncing around that much.

So, now I'm wondering if my thermostat is just fine and possibly the temperature sensor is broken or something - any thoughts/ideas/suggestions?