rubbing compaound is dangerous. it takes paint off much more quickly that t-cut (several million times more quickly)
you shouldnt t-cut where the badge was, you need to t-cut everywhere else. if you take paint off all over the tailgate it will go back to its original red colour (faded paint removed)
i would use orignal t-cut all over the tialgate first, then red colour t-cut, then a wax. it should blend in.