This sounds good, if it will work. So passing it through the LM7812 would basically reduce the voltage from 19 VDC to 12 VDC? If that's the case, I could then try it with another power supply, just to check that it works.
In the manual it says that an "additional rectifier and smoothing filter are unnecessary, as alternating current can be directly connected to the unit". Does this mean that it's not as simple as just connecting DC? Wouldn't I have to build a rectifier and smoothing filter?
Thanks for the help so far!