Female connector, 4 wires. Aveo users, does this connect or no?

[Aveo DIY Mechanic]

I've been working on diagnosing a no start situation.(new starter)

Checked all the relays, fuses, battery, starter, all good. Voltage on battery 12.6+

My last 2 hypothesis is, bad wiring (ignition to starter)/bad ignition.

I DID NOT take previous pics before doing wire/connection work (big no no), hence I'm here asking my fellow mechnic/DIY ppl about their Aveo's.

When you take of the metal plate (6 mounting bolts) from under the steering wheel, is this connector connected to a female connection, or is it, "as is", just hanging about alone unplugged?

If it DOES need to be plugged in, that will solve 50% of my issue. Pics of the connector attached. HOWEVER, the schematic for Aveo 2009 claims the ignition to battery wire is RED. When using test light, this red/white wire had "power" on it, red test light. whereas the red wire did not. This confused me, contradicts the schematic. I have a Haynes repair manual for 04-11 Aveo. The car is an 2009. I'm leaving the infomation at what i've listed to avoid any confusion. Thanks!!

[Aveo DIY Mechanic]

pic #2 hopefully