Adapting Pi to RGB modded crt

[Edgecrusher]

Hello, I'm Edge. Been lurking her trying to soak up as much info as I can and good golly there's a ton!
I am cahones deep in some arcade builds and I have collected almost half a dozen different CRT's.

For my first cabinet which is a Mrs. Pac-Man/Galaga clone I have built myself I plan to use a Rapberry Pi 4B 2Gig and a 20" CRT. Unfortunately, my two 20's only have composite and I'm not real thrilled by the picture I get using a 3.5mm jack off the PI and a converter cable. So I'd like to try a RGB mod.

I have a couple problems I can't find the answers to right off the bat.
#1. Due to the chip shortage, the usual "hat" solutions for the PI which plug on top and convert to true RGB output are not available. So I have to convert from the HDMI output.

#2. I have sourced all the schematics I need to convert to RGB but in reviewing the process I am at a loss as to what I connect the sync line to if I don't have a sync line coming from the HDMI to Composite converter I have purchased. It has R, G, B and two audio jacks. I have used this converter on a 32" Samsung I have which has the Component jacks from the factory on the back and it works. It even has a built in scaler button. However, If I RGB a CRT I will end up with four jacks but only three cables. Can someone explain how I get past this? Every mod I read gets put into a SCART connector but that's not going to work for me. Please help me wire the RGB,sync signals into a component set-up.

Here is a link to the convertor: https://www.amazon.com/Component-Conver ... s9dHJ1ZQ==