The truth is, Source 2009,2007,2006 are Singleplayer Versions of Source. Source MP is for multiplayer.
But my point is, GMod 13 does NOT treat singleplayer like singleplayer. It treats it like multiplayer but no one can connect, which is why if you pause in "singleplayer" It does not pause and theres the disconnect button.
So this means, All along YOU were using the wrong engine You actually use Source MP for gmod 13.
So here is how to configure Source SDK/MP for gmod 13
Step 1: Go to Source Engine MP in the source sdk main menu and select "Edit Game Configurations"
Then add a new one named "Garry's Mod" without quotes. Change its directory to C:/Program Files/Steam/steamapps/yoursteamusername/garrysmod/garrysmod/. And "yoursteamusername" is your Steam Username (e.g. GmodFan) XD. And BTW if you use 32-bit windows, like me use Program Files(x86)
Step 2: In the garrysmod folder (1st one not garrysmod/garrysmod/) Create a new folder named
"sourcesdk_content" without quotes then in sourcesdk_content create a folder named "mapsrc" without quotes
Step 3: Maximize Source SDK Again then open hammer with your Garry's Mod config
Step 4: Do NOT create a new map, yet we need to do one more thing thats IMPORTANT. Go To Tools/Options. then remove the FGD currently used, it's not the right one and replace the "base.fgd" with the "garrysmod.fgd" found in that garrysmod/garrysmod folder from Step 1, the FGD is at the very bottom. Select it then press Open, then when you get garrysmod.fgd rather than base.fgd, Click OK.
Step 5: Restart hammer and you are set for GMod 13 Mapping without errors!
This was how i created the map "gm_freebuildingspace" It's on the steam workshop if you want to see it or proof the config works.