My rear wiper will no longer move when the switch it turned to the ON position. If I press in the switch I can still get washer fluid onto the back window. Could this be just the relay or the rear wiper motor itself?

Probably the easiest way to check it would be to unplug the motor and measure the plug with a volt meter and see if you have voltage with the switch on. If there is no voltage it could be the switch or the realy, since the "extra push" of the switch to get the washer fluid pumpiing is actually another position of the switch. If you DO have voltage then the rear wiper motor is more than likely bad.