Apart from a brief dabble with an M&K short model in 2003, all my F1A's have been own designs with layouts based on Jim Baguley's excellent "Glider Design" series in Aeromodeller (April-December 1961), initially because I needed some F1As for the 1966 NZ Nationals but, as I couldn't get any APS plans in time, designed my own, using the Eppler E.59 section, which I used for some time in my (deservedly) little-known close-coupled Entropy design.
Its replacement, my Delta-G series which first flew in 1975, had a more conventional layout using Benedek B.84xx sections (B.8405b for the wing, B.8403 for the stabiliser) and were an obvious improvement. The only major upgrade for the next few years was a move to balsa-glass D-boxes, which made the wings much stiffer and, once I'd worked out that they needed linen thread turbulation where the rear of the LE and front of the spar had been, gave a small glide improvement.
Some time in the 1990s I needed a new stab fast, but I'd damaged the underside of my B.8403 rib template, so sanded it off to a flat bottom, leaving a roughly 7% section. To my surprise the glide was just as good and stable as before despite the new tail requiring a lot of down trim - enough to reduce the decalage by 0.5-1 degree and, as a bonus, the zoom launch was a lot faster with a more open pattern and better height gain.
The next model I built had an 8% Clark-Y section, just to see what happened. The glide remained good and the zoom got still higher and faster. I built a few like that.
When I started to use full carbon D-box wings for the series 9 models, I retained the B.8405 wing section but changed to a Woebbeking section for the stabiliser because its high point is at 15% chord. This meant I could save weight without loosing torsional stiffness by using a 15% chord carbon D-box to put the spar at maximum section thickness. Glide and launch behaviour remained close to what I'd been getting with the 8% Clark-Y tail section, but the extra wing stiffness made the launches even faster and further improved height gain.
I used to think that what stabiliser section you used was relatively unimportant provided that it was thinner than the wing and preferably from the same family of sections.
Now I think that changing the tail section has a stronger effect than I realised on longditudinal trim and can improve the model's performance in some circumstances. However, this is probably more important for models with a wide speed envelope, i.e. towline, catapult and hand-launch gliders and fast electric or IC power models, than it is for those with a narrower speed range speed such as rubber or slow-climbing power models.
None of my F1A designs used VIT, so this suggests that experimenting with the tail section may be useful for locked-up power models such as E36/F1S. As my F1A development series showed, reducing the tail section camber required a decalage reduction which did not affect glide stability but which had the beneficial effect of opening out the high speed launch pattern. If you look at the section progression: [B.8403 -> B.8403 with flat undersurface -> 8% Clark Y] the required decalage for a well trimmed glide decreased with the section's camber:
However, the Woebbeking section, which has about 4.05% undercamber at 15% of the wing chord, and performed almost identically to the 8% Clark Y, looks like an outlier compared to the other sections. These all have 7-8% thickness and a maximum camber in the range 30-40%. Since the Woebbeking section performed almost identically to the 8% Clark Y, it clearly has different aerodynamics.
So, varying the tail section used on an F1S or a locked-up power model so as to incrementally vary its camber line would appear to offer a fairly benign way to tune the power pattern to suit the model's climb rate.