amp relay

Somehow the Remote-on lead on my amp doesn't work anymore.  When connected, the amp stays powered on regardless of the car being on or off.  I've tried everything to fix the problem, measure all the volts using a multimeter, and have come to the conclusion that it's the Remote-on lead on the amp itself.  The amp still works fine, and powers the subs fine.  It'll just drain the battery unless I connect it.

 

So my question is, to avoid having to purchase another amp, can I use a relay and put it in the 12V power cable (8ga), run the remote-on wire to it to trigger the switch, ground the relay, and then run the other part of (8ga) 12V power cable to my amp?  Would this work?  I'm not wanting to add the relay to the remote-on wire itself, I want to add it to the main power wire, so the amp would NOT have the remote-on wire connected to it period, yet the amp would turn on and off whenever the car did so.  Any help would be greatly appreciated!