I have a RHD TJ (in Australia), so we drive on the left hand side of the road too.
If what you are describing is a gradual wander to the left (not a sudden veer) then we all experience it down here as well.
One theory put forward is that most roads aren't flat. The middle of the road is slightly higher than the edges to help with rain run-off, so we are constantly driving on a slight incline.
In Australia, we have some VERY LONG stretches of straight road with almost no traffic, so I did an experiment driving on the right hand side of the road.
All tests done at 50 - 60 mph.
Occasionally the Jeep would veer to the right.
Mostly though, it was just much less inclined to veer to the left and would go dead straight for ages but would eventually (and much more slowly) veer left until the Jeep wandered over the middle of the road (to the left hand side) , then the veer would become more pronounced.
Other problems like losing pressure or alignment would also add to the problem.
Spray some soapy water on the valves (or around the bead) if the soapy water bubbles, you have found your leak.