I see the red and what audio cables on the TV connected to the INPUT TO THE TV.

Wouldn't you need an OUTPUT?

The full TV model was in the pictures (those trailing letters) so I'll read

This model has ZERO audio outputs. No analog or optical.
"Inputs & Outputs
Ethernet Yes
Component 1
Composite In (AV) 1, 1 (back shared with component)
RF In (Terrestrial/Cable Input) 1 "

So this is a model that will never work with your wireless headphones.

--> Now not all is lost. If you feed your TV with a HDMI source you can split off the audio with the usual HDMI SPLITTER.

There are now dozens of these boxes so here's one as an example on Amazon.