First, if you don't already have it, download the latest fully functional version of AmaRecTV (3.10): https://www.videohelp.com/download/amarectv310.zip
Be sure to configure the program to your liking.
In the .ZIP file, there's "live_setup300.EXE", run it and install, the installed program should go into your Program Files (x86) folder under "AmaRecTV Live".
After that's successfully installed, you need to download the new version of AmaRecTV Live, (4.11 beta): http://www.amarectv.com/download/live411beta.zip
Copy the contents of the folder contained in the .ZIP file into your AmaRecTV Live installation.
Next, run "live411_install.bat" as administrator. From the previous version of AmaRecTV Live, there's the file "register.bat", you must edit it to include the 64 bit files from the 4.11 installation:
AmAudioCapture64.ax AmVideoCapture64.ax
Saving the edited .BAT file to the same directory may not be possible, so save it to your desktop (or some other location), then copy it to the directory, replacing the old one. Then, run "register.bat" as administrator. You may get an error message or two, but that is just because it attempts to reference .AX files that don't exist. Next, open your installation of AmaRecTV, configure and enable live.
AmaRecTV Live should now be accessible in the 64 bit version of OBS Studio, as well as other supported 64 bit applications. As usual, AmaRec and its Live component may require some troubleshooting, but I've attached a screenshot to prove this method works, at least on Windows 10 Pro 64 bit with my EasyCap (STK1160).
UPDATE: I've found that in OBS, right clicking "Video Capture Device" -> "Properties" and then changing "Resolution/FPS Type" from "Device Default" to "Custom" and back again consistently fixes the problem where it only shows the AmaRecTV Live splash screen.