Been a while so here is a quick update:
The USB camera never worked with the configuration I was forcing upon it, I gave up on trying the USB splitter.
I ordered this little thing
on Amazon. I was excited to get it, plugged it in, and got a picture on the TV! I was stoked! ...until the picture went blue. ?!?! I jiggled the wires a bit and the picture came back on. Ok, I thought, stay calm, this will work.
Like Chuck Testa, "NOPE!"
The picture died again, and the sound never worked. Ugh. I went right to the computer and filed for crappy parts and how to return it. Thankfully, Amazon has a generous return policy (and I have Prime). A replacement part was shipped the next day, and all I had to do was to ensure I returned the first broken one.
The new camera arrived , I plugged it in, Shazam! Picture, check. Sound, check-1-2-check. I let out a sigh of relief knowing I have a working part and can move forward. Next task, build a small hand-held unit to house the camera and keep the wiring safe.