What you are looking for is a HDMI audio extractor. These are readily available on Amazon, but you will want to be aware of whether you are working with 1080p video or 4K HDR video. The HDMI audio extractors also may have multiple inputs so they will act as both a HDMI switcher as well as a HDMI audio extractor at the same time.
The difference between 1080p video connectivity and 4KHDR is that one connection is older and less money, while the newer 4K standard will require a HDMI setup that supports 18Gb/s.
Without getting a switcher built in, a unit like this is rated to support 4KHDR...
Amazon.com: WyreStorm Essentials Analog & Digital Audio Extractor with HDMI Passthrough and Audio EDID Management: Home Audio & Theater
www.amazon.com
or
Amazon.com: gofanco Prophecy 4K 60Hz HDMI Audio Extractor & Embedder via S/PDIF Toslink + 3.5 MM Stereo, 4K 60Hz YUV 4:4:4, HDR, HDMI 2.0a, HDCP 2.2, 18Gbps, ARC, CEC, Audio Extraction & Embedded: Electronics
www.amazon.com
You will note that it offers the Red/White analog RCA outputs you are looking for. A dip switch on one side of the unit will let your source gear know that you want 2 channel stereo (instead of surround sound).
A unit like this is LESS expensive and has support for 3 HDMI sources and integrates the audio extraction. It is what I would buy.
Buy J-Tech Digital HDMI Audio Extractor 4K@60Hz 4:4:4 3X1 Switcher SPDIF + L/R RCA Outputs with ARC Auto Switch EDID HDMI 2.0, 18Gbps, HDCP 2.2, Dolby Passthrough CEC, HDR10, Dolby Vision [JTECH-SWE31]: Selector Switch Boxes - Amazon.com ✓ FREE DELIVERY possible on eligible purchases
www.amazon.com
It should be noted that for about $300 you can buy a AV receiver which fully supports stereo, surround sound, has multiple HDMI inputs, and will be more reliable overall.