There are two approaches that should work for you.
You can apply a real “Transition” effect from Vegas’s transition palette as a one-sided transition to just the front edge of the graphic. As a one-sided wipe this would transition between “nothing” and the graphic - so it would wipe on automatically
Alternatively you could apply a wipe effect from the Video Event Fx palette to the graphic. Then you need to change the Animation menu near the top of the effect from Auto to Manual. You can then keyframe the Percent Done slider manually so that the graphic wipes on and holds.