My 2017 Adventurer has a HDMI source selector that looks like a radio head unit. It's mounted in a panel below the bedroom TV and next to an open shelf used for SAT receivers and DVD players. There is a separate wooden panel that is screwed into the overall cabinet. There are 4-screws, one in each corner, holding the panel to the cabinet. The HDMI source selector (it's an Ethernet to HDMI convertor) is installed in that panel.
I tried to look at the wiring diagrams for your 2005 but didn't see anything.
2017 Winnebago Adventurer 37F
2016 Lincoln MKX Toad