Can I additionally connect an existing RCA input, reverse-light-wired backup camera to an always-on monitor?

I recently bought these two products:

• https://www.bestbuy.com/site/pioneer-6-8-amazon-alexa-apple-carplay-android-auto-bluetooth-and-siriusxm-ready-multimedia-dvd-receiver-black/6328679.p?skuId=6328679
• https://www.amazon.com/gp/product/B074KZSVD6/ref=ppx_yo_dt_b_asin_title_o00_s00?ie=UTF8&psc=1

I installed them successfully.

Then, I bought this:

• https://www.amazon.com/12-Mirror-Dash-Cam-Waterproof/dp/B08V8NHKF3/ref=sr_1_4?dchild=1&keywords=vantop%5C&qid=1627301692&sr=8-4

Now, the rear view monitor/dash cam directly above comes with a backup camera, but I would like to avoid installing it and instead simply use the camera I already installed.

The video cable from the existing camera is a yellow RCA, and the input for the new display is 3.5mm jack. So at a minimum, I think I would need an RCA splitter, and a cable that was RCA on one end and 3.5mm on the other end.

The part I’m not sure of is the always-on nature of the rear-view mirror display, vs. the reverse-light-trigger that my existing camera uses.

If I just fed the video signal from my existing camera to the new rear-view display, would it only show when the car was in reverse? Or is the video signal transmitted regardless?