I'd pull the RCM and have it gone over with a soldering iron before ordering a Pulse Module. In all my time here, I cannot remember anyone having a bad pulse module.

That is, of course, after going over the battery terminal connections - and just as a 'mention', my car's battery ground cable had corroded all to hell at the chassis end - I didn't find it until I replaced the battery. $12 for a generic one at AutoZone.