I need to find an "off-on-on" type switch that goes like this:

[down]: Headlights and running lights are off.
[middle]: Power goes to running lights.
[up]: Power keeps going to running lights, but also goes to headlights.

Does a switch like this exist?

It seems like if I just make a split in the running light wire, and attach one end of the split to the middle position terminal, and the other to the top position terminal, then run the headlights wire to the top position terminal, that the headlights would come on when the switch is in middle or up position seeing as they are technically connected via the split in the running light wire like in my super-advanced diagram below. Am I right?

 

well the best I can think of is using the 3 way switch that goes middle is neutral, Down is on and Up is on. Just wire the bottom position to the running lights then on top switch run a wire to the head lights and then patch into the running light wire. This way you have fire to the running lights on both positions but only to the headlights in the up position. In essence thats pretty much how the factory set up is. Dont forget to put fuses on these lines as well. Dont want your car to catch fire from a short or something.