The technical answer can be found in
Fluid Dynamic Drag by Hoerner. It is experimentally determined, but is a decent balance between frontal area and eliminate vortex inducing corners. The reason it doesn't depend on span or body tube diameter is because it is a very local effect. Unless the span is <~10% of the root, the air can't tell how long the span its, it may as well be infinite. For rocket fins span is typically at 50-150% of the root chord.
The problem is that it depends on just how you interpret Hoerner's data. The rule of thumb first cited by Stine and repeated by others comes from a chart in Chapter 8 of my edition which applies to airplane struts that have a t/c ratio of about 0.3.
However, earlier in the chapter (I don't have it in front of me right now) is a chart and relevant discussion in which Hoerner strongly implies that for airfoils with a very low t/c, fillets are at best worthless for reducing drag and at worst can increase drag. Since most rocket fins have very low t/c ratios, I tend to think that a proper reading of Hoerner would indicate that external fillets should
Be no larger than is required for structural integrity.
When I point this out I generally find that nobody changes their minds but also that nobody can come up with a rebuttal to the argument. So I guess you should do what makes you feel good. Without hard data for a configuration similar to the one we typically deal with in rocketry it will probably continue to be a religious argument.
I had been wondering about this as well. Is the optimum fillet radius for a Hi-Flier really several times that for a Wizard, for example? So, earlier today, I searched and found this thread. Just went through Chapter 8 of Hoerner.
The 4-8% rule of thumb is suggested on p. 8-12, in the text above Figure 29, which is the basis for it.
The general discussion in that section of the chapter, however, is dealing with thick wing airfoil sections and struts having thickness/chord (t/c) ratios of (to report specific examples discussed in the paper) 0.3 (Figure 27) and 0.435 (Figure 30). As Bill Cook points out, Figure 26 indicates that the interference drag becomes very small for t/c ratios below 0.1, with a zero crossing around t/c = 0.5-0.6. With smaller t/c ratios, the interference drag is graphed as negative and there is no differentiation below the zero crossing between with and without fillet.
On p. 8-16, discussing
(c) Tail Surfaces, Hoerner points out that Figure 34 indicates again that interference drag on horizontal stabilizer surfaces at the very aft end of a fuselage can actually be negative at zero lift with a crossing (zero) point around 2 degrees angle of incidence.
I agree that this all supports that, "external [model rocket fin] fillets should be no larger than is required for structural integrity." They add weight to the wrong end of the rocket while increasing frontal area, with the aerodynamic advantages, if any, being minimal.
A survey of full-scale sounding rocket and missile fins suggests that fillets are simply not a thing in that world, where vast resources are available to optimize the designs and adding something like fillets would be an easy way to increase performance (on which hangs life/death and the fate of nations, or otherwise substantial sums of money) if it worked.
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