I use an HDMI switch box. One input and multiple outputs. There are manual ones that you have to switch, one's with remotes and one that detects what's feeding it and switches automatically. This might work as it has two inputs and multiple outs.
Example:
https://www.amazon.com/ZAMO-Switcher...ps%2C66&sr=8-8
【HDMI Switch 2 in 4 out HDCP 2.2】avedio links hdmi 2 input 4 output 2X4 switcher splitter can easily streams video and audio from 2 HDMI devices to 4 HDMI display simultaneously .Supports HDCP 2.2 protocol compliant HDMI 2.0（Note: The four HDMI output ports can only display the same screen and split display is not supported.）
【Vedio &Audio】4K HDMI Switch Selector box supports up to Ultra HD 4k@60Hz resolution RGB/YUV 4:4:4 .,4k@30hz,Full HD 1080P,720P,3D, HDMI 2.0, It also supports 3.5mm and SPDIF audio output.
【Wide Compatibility】 avedio links 2x4 HDMI switch box compatible with computer, Blu-ray player, DVD player, AV receiver, Roku streaming media player, TV Box, Play Station 3/4, PS5, Xbox One/360 or other HDMI compatible devices to your Ultra 4K TV (UHD TV), HDTV, monitor, display or projector with a big screen.
【Features】DOWNSCALING:avedio links HDMI switch 2 in 4 out can output 4k and 1080p at the same time.HDR 10: Help you enjoy a vivid visual world! All ZAMO products are backed by our 12-Month Product Warranty and you will always get friendly support.
【Plug and Play】 This 4K HDMI Switch is easy to set up and operate, just power it with AC adapter and connect your HDMI devices to enjoy! TWO-WAY SWITCH:Supports manual select input sources through a built-in button or use of IR remote controller without having to get up from your seat.