Please excuse me if I state obvious things or areas you have already gone over. I'm a new owner of a 2005 Adventurer 37B and am using your problem to increase my knowledge. If you don't have wiring diagrams go to http://omeys-performance.com
under downloads on the left you can go to OEM Chassis Related Documnets<sic> and see 2005 W22 and W24 electrical diagrams. You will want to download both of them. On the W22 diagram go to page 6 of 52 (Sheet10, page 2 of 5, area5-B) and you can see Fuse 16. The output from the fuse 16 leaves the block on connector C254 on a yellow wire with the (hopefully) label X43 (Sheet 204, page 1 of 2; see page 46 of 52) Directly to Conv CTR on Sheet 013-1. Now the rub; the W22 diagram on Omey's site is missing Sheet number 13, I/P Extn Convenience Center, and page 2 of this should have a pictorial and Body builder Information. (If someone knows where this is available, please chime in). But going to the W24 diagram from Omey's it does have Sheet 13 (sorta). Open the W24 diagram and go to page 5 of 10 (Dwg 148600, Sheet 2) and Area 2-D has the connector "E" in the convenience center with your wire "LD" on pin 1. It is even possible that the pictorial is what your connector looks like. If Winnie or Workhorse can come up with the diagrams for you, or another member has a reference, please post a follow-up. Hope some of this helps.