You should be able to just connect the component connector from the Tivo to the Avant. You probably do need to select 480p output on the Tivo. The Avant cannot downscale like more modern tvs do.
The 5 connector BNC was more common back when the Avant was introduced. BNC and VGA were common connectors for projectors back then. This got VERY frustrating with the BeoSystem 1 -- which is basically the Avant chassis without the tv screen. It was nearly impossible to find third party tv screens that were compatible with the BeoSystem 1 requirement for VGA or B,R,G,H,V.
Something worth mentioning is that many of the earlier Avants were prone to getting a horrible magenta hue with video content going through the HD input. The Avant came out at a time when HD was still in its infancy and the Avant often had this fault. Sometime the magenta hue would happen after awhile. Unplugging the Avant and the source device from the power and restoring power often set the video back to normal --- until the magenta hue returned later.