A thinner béarnaise? I've been using Julia Child's béarnaise recipe---2 tbl reduction, 3 egg
yolks, 4 oz clarified butter---, which produces a very thick sauce.  Is
this just how it's supposed to be, or is there a non-heretic way of
making it thinner?
The thickness is coming from the ratio of oil to water. Like mayonnaise, bearnaise is an oil-in-water emulsion, and will get thinner the more water is in it. (Consider the relative thickness of moist sand and mud; the butter in the bearnaise is like the sand.) Adding a bit of hot water will work well to thin it, but do so a bit at a time, stirring well afterwards, as a little bit of water will go a long way.