Hi,
I have a similar issue to the issues described above. It's a 2007 Dodge Durango, 5.7L Hemi. It has the two relay like boxes on the driver's side, with the TIPM (I guess, same number, P04692) toward the front. Initially had some strange issues. Found eventually a dead battery. That led to the need for a new alternator (low voltage when running). Then when truck was left alone for awhile, battery would go to 0. Found that fuel and ASD relays would chatter intermittently, running battery down.
Charged battery up, was able to start it. Then stopped it for awhile. Then relay chattering started again. Here's a tip, when you can't start it: Remove the ground cable from the battery for a few minutes and then reattach. Each time i've done this i get different results. Many times it seems like it's ok and even can start and run. But after a while the freakiness starts again. I think it's the TIPM. I swapped relays around in case there was a contact or relay issue to no avail. I took most of it apart and reseated all connections, removed and polished up the ground near the sidewall. But same effect. Tomorrow i hope to be able to get a TIPM module from the dealer (assuming it's a few hundred and not 1200). We'll see.
Any other ideas?