I'd recommend searching for HDMI Switcher (Off-Topic)

by Cody Miller , Music of the Spheres - Never Forgot, Sunday, September 30, 2018, 09:24 (2246 days ago) @ Xenos
edited by Cody Miller, Sunday, September 30, 2018, 09:27

Splitter can refer to outputting one HDMI output to two ports, but they visually look like they'd work so just to avoid confusion look for an HDMI switcher. You can find well reviewed ones for $20 or less.

Here's one with 4 1/2 stars (with 160 reviews) for less than $7:

https://www.amazon.com/Splitter-GANA-Bidirectional-Supports-Passthrough-HDMI/dp/B07BFVN6GY

Funny enough it works as both a splitter or a switcher.

I have a ViewHD VHD-1X2MN3D splitter. There is no latency at all. But the real reason I have it? It strips HDCP! But a switcher is what you want. A splitter takes one input and turns it into two outputs.