No, not much to do with dihedral, David, but another factor to be considered. Andy Lennon's R/C Model Aircraft Design speaks to horizontal tail airfoils in this way.
"Since the horizontal tail surface has to provide lift - both up and down - symmetrical airfoils such as Eppler E168 are recommended."
That is a roughly 12.5% airfoil - confirming George's hunch that a thinner airfoil is suggested for the horizontal stab. Lennon does not advocate flat plate (aka slab) airfoils in that they are less effective than symmetrical airfoils.
Jim Kirkland's Intruder made use of a "diamond" airfoil section. This is what he had to say:
"For a given stab section, a rounded leading edge decreases elevator sensitivity around neutral, while a sharper leading edge increases sensitivity around neutral. Stabilizer thickness governs the elevator's sensitivity away from the neutral zone, contributes to tail drag coefficient, and is a factor in determining the amount of elevator deflection requirements. The curvature of the airfoil did not seem to matter very much!
"So why bother to jig-up and build a symmetrical airfoil stab, when the airfoil curvature played so little a part in the overall performance? ... The result ... became the diamond stab section used first on the Triton, and further refined on the Intruder.
"Ed Kazmirski used a diamond stab section on the Taurus, and I suspect for the same reason that I finally selected such a section for use on the Triton."
At the risk of thread-creep, I'll scan and post how a diamond-section stab is built...
[8D]
PJ