Automotive circuit works but with lots of heat. Is there a better way?
From your description of what the tow vehicle is doing, it sounds like all you need to do is put a capacitor in series with the 8&Omega; resistor. This would allow the 5V "test" pulses to pass through the resistor, but block any steady-state dissipation when 12VDC is applied.

Can you use an oscilloscope to measure the period and pulse width of the test pulses? This would give you the information needed to calculate the value of the capacitor to use. You want to pick the value such that the R-C time constant (with the 8&Omega; resistor) is the same order of magnitude as the pulse width.

For example, if the pulse is 100&micro;s wide, you would calculate the capacitor value to be:

C = t/R = 100&micro;s/8&Omega; = 12.5&micro;F

Either 10&micro;F or 15&micro;F would probably work fine.

Note that the capacitor discharges through the relay coil in between test pulses.