Cannot reach Recovery mode to switch from External boot up drive to internal boot up drive

I have a 2009 iMac running El Capitan. The current hard drive running the OS is external. I want to switch back to the internal drive. Disk Utility has allowed me to mount, erase, and repair the internal drive. It appears to be ready for use. Since the internal drive is mounted I thought I could use Recovery mode to switch to the internal drive and give instruction to restore the OS and all other files from my time machine backup. I have been trying to get to Recovery mode by restarting and holding Command + R as well as Command + R + option but instead of Recovery mode the computer brings me back to the user sign in screen. Am I going about this wrong? Is there another way? The Apple Community has been a great resource in the past and any help would be much appreciated.