There are plenty of circuits for the rear markers that would light up all the time, and also the reverse light. As far as LED's, see my previous post about the 220 ohm resistor. However, the marker light outputs are already current limited for LED's, but they usually wire two LED's in series, so I'd still stick a resistor in there.
If you buy the illuminated number boards and can fit them, you may have to tap off the headlight for them, or perhaps the flickering firebox output. Worst come to worst, you can also just power them from track power. In the user's manual for the 2002 model, they mention running the lights off a CV board. Those typically can have outputs for extra lighting, you may have to add a Molex socket to plug in the number boards if it's equipped with the CV board.